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		<updated>2026-05-13T08:07:10Z</updated>
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		<id>https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57016&amp;oldid=prev</id>
		<title>Madhurig at 11:37, 8 July 2025</title>
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				<updated>2025-07-08T11:37:01Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 11:37, 8 July 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 187:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 187:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Show the Correlation matrix output 4.47&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Show the Correlation matrix output 4.47&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|| Here, experience and income have a correlation of '''0.97.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;|| Here, experience and income have a correlation of '''0.97.'''&lt;/del&gt;This means that as &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;'''&lt;/del&gt;experience increases&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;'''&lt;/del&gt;, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;'''&lt;/del&gt;income also increases&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;''' &lt;/del&gt;strongly.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This means that as experience increases, income also increases strongly.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let us understand the correlation value ranges.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let us understand the correlation value ranges.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 255:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 256:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Highlight the lines:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Highlight the lines:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Then, we split the data into '''training''' and '''testing''' '''sets'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Then, we split the data into '''training''' and '''testing''' '''sets'''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 487:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 487:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Narration&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Narration&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| The model has an '''MAE''' of '''1700.15''', showing the average prediction error in income.The '''Adjusted R squared score''' is '''0.921'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| The model has an '''MAE''' of '''1700.15''', showing the average prediction error in income.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The '''Adjusted R squared score''' is '''0.921'''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;It indicates the model explains '''92.1 percent''' of income variance.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;It indicates the model explains '''92.1 percent''' of income variance.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Madhurig</name></author>	</entry>

	<entry>
		<id>https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57015&amp;oldid=prev</id>
		<title>Madhurig at 10:28, 7 July 2025</title>
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				<updated>2025-07-07T10:28:51Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:28, 7 July 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
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&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| border=&amp;quot;1&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| border=&amp;quot;1&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 9:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Show slide:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Show slide:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Welcome''' &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Welcome'''&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Welcome to the Spoken Tutorial on '''Linear Regression'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Welcome to the Spoken Tutorial on''' Linear Regression'''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Madhurig</name></author>	</entry>

	<entry>
		<id>https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57014&amp;oldid=prev</id>
		<title>Madhurig at 10:21, 7 July 2025</title>
		<link rel="alternate" type="text/html" href="https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57014&amp;oldid=prev"/>
				<updated>2025-07-07T10:21:46Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
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				&lt;col class='diff-content' /&gt;
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				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:21, 7 July 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| border=&amp;quot;1&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| border=&amp;quot;1&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 9:&lt;/td&gt;
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&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Show slide:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Show slide:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Welcome'''&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Welcome''' &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Welcome to the Spoken Tutorial on''' Linear Regression'''.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|| Welcome to the Spoken Tutorial on '''Linear Regression'''.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Madhurig</name></author>	</entry>

	<entry>
		<id>https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57010&amp;oldid=prev</id>
		<title>Madhurig at 10:28, 4 July 2025</title>
		<link rel="alternate" type="text/html" href="https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57010&amp;oldid=prev"/>
				<updated>2025-07-04T10:28:15Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
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				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:28, 4 July 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Madhurig</name></author>	</entry>

	<entry>
		<id>https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57008&amp;oldid=prev</id>
		<title>Madhurig at 10:18, 4 July 2025</title>
		<link rel="alternate" type="text/html" href="https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=57008&amp;oldid=prev"/>
				<updated>2025-07-04T10:18:00Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;a href=&quot;https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;amp;diff=57008&amp;amp;oldid=56989&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Madhurig</name></author>	</entry>

	<entry>
		<id>https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=56989&amp;oldid=prev</id>
		<title>Nirmala Venkat: Created page with &quot;  &lt;div style=&quot;margin-left:1.27cm;margin-right:0cm;&quot;&gt;&lt;/div&gt; {| border=&quot;1&quot; |- || '''Visual Cue''' || '''Narration''' |- |- style=&quot;border:0.5pt solid #000000;padding-top:0cm;padd...&quot;</title>
		<link rel="alternate" type="text/html" href="https://script.spoken-tutorial.org/index.php?title=Python-for-Machine-Learning/C2/Linear-Regression/English&amp;diff=56989&amp;oldid=prev"/>
				<updated>2025-06-19T10:20:07Z</updated>
		
		<summary type="html">&lt;p&gt;Created page with &amp;quot;  &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;/div&amp;gt; {| border=&amp;quot;1&amp;quot; |- || &amp;#039;&amp;#039;&amp;#039;Visual Cue&amp;#039;&amp;#039;&amp;#039; || &amp;#039;&amp;#039;&amp;#039;Narration&amp;#039;&amp;#039;&amp;#039; |- |- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padd...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
{| border=&amp;quot;1&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
|| '''Visual Cue'''&lt;br /&gt;
|| '''Narration'''&lt;br /&gt;
|-&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| &amp;lt;div style=&amp;quot;color:#000000;&amp;quot;&amp;gt;Show slide:&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div style=&amp;quot;color:#000000;&amp;quot;&amp;gt;'''Welcome'''&amp;lt;/div&amp;gt;&lt;br /&gt;
|| Welcome to the Spoken Tutorial on''' Linear Regression'''.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide: &lt;br /&gt;
&lt;br /&gt;
'''Learning Objectives'''&lt;br /&gt;
&lt;br /&gt;
|| In this tutorial, we will learn about&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;color:#000000;&amp;quot;&amp;gt;'''Linear Regression'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;color:#000000;&amp;quot;&amp;gt;'''Simple Linear Regression'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;'''Multiple Linear Regression'''&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;color:#000000;&amp;quot;&amp;gt;'''Evaluation Metrics'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide: &lt;br /&gt;
&lt;br /&gt;
'''System Requirements'''&lt;br /&gt;
&lt;br /&gt;
|| To Record this tutorial, I am using&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;color:#000000;&amp;quot;&amp;gt;'''Ubuntu Linux operating system 24.04'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''Jupyter Notebook'''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt; &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''IDE'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide: &lt;br /&gt;
&lt;br /&gt;
'''Prerequisite'''&lt;br /&gt;
|| To follow this tutorial,&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;The learner must have basic knowledge of &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''Python.'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;For prerequisite '''Python''' tutorials, please visit this website.&amp;lt;/div&amp;gt;&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide:&lt;br /&gt;
&lt;br /&gt;
'''Code files'''&lt;br /&gt;
||&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;The files used in this tutorial are provided in the &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''Code files '''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;link.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#252525;&amp;quot;&amp;gt;Please download and extract the files.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#252525;&amp;quot;&amp;gt;Make a copy and then use them while practicing.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide: &lt;br /&gt;
&lt;br /&gt;
'''Linear Regression'''&lt;br /&gt;
&lt;br /&gt;
|| &lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;'''Linear regression''' is a predictive technique used in machine learning. &amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;It builds the relationship between a '''dependent''' and '''independent''' variable.&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;Linear regression is categorized into &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''Simple'''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt; and &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''Multiple linear regression'''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide: &lt;br /&gt;
&lt;br /&gt;
'''Simple Linear Regression'''&lt;br /&gt;
&lt;br /&gt;
|| &lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt;'''Simple Linear Regression '''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt;is a way to find &amp;lt;/span&amp;gt;relationships&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt; between two variables.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;It studies how one '''independent variable''' affects one '''dependent variable'''.&amp;lt;/div&amp;gt;&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide: &lt;br /&gt;
&lt;br /&gt;
'''Multiple Linear Regression'''&lt;br /&gt;
||&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt;'''Multiple linear Regression'''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt; is an extension of simple linear regression.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;It examines how multiple factors influence a single outcome.&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide:&lt;br /&gt;
&lt;br /&gt;
'''Evaluation Metrics'''&lt;br /&gt;
||&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;To assess the model’s performance, we use '''evaluation metrics'''.&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;These metrics indicate how well the '''regression model''' fits the data. &amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt;The two common metrics are &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt;'''Mean Absolute Error '''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt;and &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;&amp;quot;&amp;gt;'''R squared score.'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Hover over the files&lt;br /&gt;
|| I have created required files for the demonstration of''' Linear Regression.'''&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Open the file salaries.csv and point to the fields as per narration.&lt;br /&gt;
&lt;br /&gt;
Open the file salaries_mlr.csv and point to the fields as per narration.&lt;br /&gt;
|| To implement '''Simple Linear Regression''', we use the '''salaries dot csv '''dataset.&lt;br /&gt;
&lt;br /&gt;
This dataset contains salaries based on years of experience.&lt;br /&gt;
&lt;br /&gt;
We use '''salaries underscore mlr dot csv''' dataset for '''Multiple Linear Regression.'''&lt;br /&gt;
&lt;br /&gt;
This dataset contains multiple columns as shown.&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Point to the '''LinearRegression.ipynb '''&lt;br /&gt;
|| '''LinearRegression dot ipynb '''is the python notebook file for this demonstration.&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Press '''Ctrl,Alt'''+'''T '''keys&lt;br /&gt;
&lt;br /&gt;
Type '''conda activate ml'''&lt;br /&gt;
&lt;br /&gt;
Press '''Enter'''&lt;br /&gt;
|| Let us open the Linux terminal. Press '''Ctrl, Alt''' and '''T '''keys together.&lt;br /&gt;
&lt;br /&gt;
First, we need to activate the machine learning environment. &lt;br /&gt;
&lt;br /&gt;
Run the command '''conda space activate''' '''space ml.'''&lt;br /&gt;
&lt;br /&gt;
Press '''Enter.'''&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Go to the '''Downloads '''folder&lt;br /&gt;
&lt;br /&gt;
Type '''cd Downloads'''&lt;br /&gt;
&lt;br /&gt;
Press '''Enter '''&lt;br /&gt;
&lt;br /&gt;
Type '''jupyter notebook'''&lt;br /&gt;
&lt;br /&gt;
Press '''Enter '''&lt;br /&gt;
|| I have saved my code file in the '''Downloads''' folder. &lt;br /&gt;
&lt;br /&gt;
Please navigate to the respective folder of your code file location.&lt;br /&gt;
&lt;br /&gt;
Then type, '''jupyter space notebook and''' press''' Enter.'''&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show '''Jupyter Notebook Home page'''&lt;br /&gt;
&lt;br /&gt;
Click on'''LinearRegression.ipynb file'''&lt;br /&gt;
|| We see the '''Jupyter Notebook''' Home page.&lt;br /&gt;
&lt;br /&gt;
Click the '''LinearRegression dot ipynb''' file to open it.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div style=&amp;quot;color:#000000;&amp;quot;&amp;gt;Note that each cell will have the output displayed in this file.&amp;lt;/div&amp;gt;&lt;br /&gt;
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|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''import numpy as np '''&lt;br /&gt;
&lt;br /&gt;
'''import pandas as pd '''&lt;br /&gt;
&lt;br /&gt;
Press '''Shift+Enter'''&lt;br /&gt;
&lt;br /&gt;
|| We start by importing the required libraries for '''Simple''' '''Linear''' '''Regression'''.&lt;br /&gt;
&lt;br /&gt;
Make sure to Press''' Shift '''and''' Enter''' to execute the code in each cell.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''df_salary=pd.read_csv(&amp;quot;salaries.csv&amp;quot;) '''&lt;br /&gt;
&lt;br /&gt;
|| Let us load the dataset into a variable called '''df underscore salary.'''&lt;br /&gt;
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|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''df_salary.head()'''&lt;br /&gt;
&lt;br /&gt;
|| Next, we display the '''first few rows''' of the data.&lt;br /&gt;
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|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''df_salary.describe()'''&lt;br /&gt;
&lt;br /&gt;
|| Now, we generate '''summary statistics''' for the numerical columns.&lt;br /&gt;
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|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''sns.heatmap(df_salary.corr(), annot=True, cmap=&amp;quot;coolwarm&amp;quot;) '''&lt;br /&gt;
&lt;br /&gt;
'''plt.show() '''&lt;br /&gt;
&lt;br /&gt;
|| '''Correlation heatmap''' shows how attributes in the dataset are related.&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Narration:&lt;br /&gt;
|| '''Correlation''' measures how two variables are related to each other.&lt;br /&gt;
&lt;br /&gt;
'''Correlation''' measures the relationship between two variables&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div style=&amp;quot;color:#000000;&amp;quot;&amp;gt;The '''correlation''' '''values range from -1 to 1'''.&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show the Correlation matrix output 4.47&lt;br /&gt;
&lt;br /&gt;
|| &amp;lt;div style=&amp;quot;color:#000000;&amp;quot;&amp;gt;Here, experience and income have a correlation of '''0.97.'''This means that as '''experience increases''', '''income also increases''' strongly.&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Let us understand the correlation value ranges.&lt;br /&gt;
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|| Show Slide:&lt;br /&gt;
&lt;br /&gt;
'''Correlation Matrix'''&lt;br /&gt;
||&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;A value of '''1''' means a '''perfect''' '''positive correlation'''.&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;A value of '''-1''' means a '''perfect negative correlation'''.&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;A value of '''0 '''means '''no correlation'''&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''plt.figure(figsize=(6,4)) '''&lt;br /&gt;
&lt;br /&gt;
|| Now we create a '''boxplot''' to visualize the income distribution.&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show the output&lt;br /&gt;
&lt;br /&gt;
|| This image is a boxplot of income '''before removing outliers.'''&lt;br /&gt;
&lt;br /&gt;
'''Outliers''' are extreme values that differ significantly from other data points.&lt;br /&gt;
&lt;br /&gt;
They are the small circles on the right side of the boxplot.&lt;br /&gt;
&lt;br /&gt;
Here, incomes around 60,000 to 65,000 are considered as outliers.&lt;br /&gt;
&lt;br /&gt;
The line inside the box is the '''median'''.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;nowiki&amp;gt;Q1 = df_salary[['experience', &amp;lt;/nowiki&amp;gt;'income']].quantile(0.25) &amp;amp;nbsp;'''&lt;br /&gt;
&lt;br /&gt;
'''&amp;lt;nowiki&amp;gt;Q3 = df_salary[['experience', 'income']].&amp;lt;/nowiki&amp;gt;quantile(0.75) &amp;amp;nbsp;'''&lt;br /&gt;
&lt;br /&gt;
'''IQR = Q3 - Q1 '''&lt;br /&gt;
&lt;br /&gt;
|| Next, we will '''remove these outliers''' using the '''Interquartile Range''' method.&lt;br /&gt;
&lt;br /&gt;
We calculate '''first quartile Q1''' and '''third quartile Q3''' for experience and income.&lt;br /&gt;
&lt;br /&gt;
Then, we compute the''' IQR '''and remove the outliers.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''plt.figure(figsize=(6,4)) '''&lt;br /&gt;
&lt;br /&gt;
|| Now, we plot the income distribution after '''removing outliers'''.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show the output&lt;br /&gt;
&lt;br /&gt;
|| Observe that the small circles are gone, showing outliers were removed.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''x=df_salary['experience'] '''&lt;br /&gt;
&lt;br /&gt;
'''y=df_salary['income'] '''&lt;br /&gt;
|| Now, we define '''x''' as '''experience''' and '''y''' as '''income''' from the dataset.&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
|| Then, we split the data into '''training''' and '''testing''' '''sets'''.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''x_train=np.array(x_train).reshape(-1,1) '''&lt;br /&gt;
&lt;br /&gt;
'''x_test=np.array(x_test).reshape(-1,1)''' &lt;br /&gt;
|| We then reshape the '''x underscore train''' lists into '''2D array.'''&lt;br /&gt;
&lt;br /&gt;
The same is done for '''x underscore test''' for '''compatibility.'''&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''lr=LinearRegression() '''&lt;br /&gt;
&lt;br /&gt;
'''lr.fit(x_train,y_train)'''&lt;br /&gt;
&lt;br /&gt;
|| Now, we initialize a '''Linear Regression model''' and train it using training data.&lt;br /&gt;
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|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''print(&amp;quot;Intercept (W0):&amp;quot;, lr.intercept_)'''&lt;br /&gt;
&lt;br /&gt;
'''print(&amp;quot;Coefficient (W1):&amp;quot;, lr.coef_)'''&lt;br /&gt;
&lt;br /&gt;
|| Then, we print the '''intercept W0''' and '''coefficient W1''' of the model.&lt;br /&gt;
&lt;br /&gt;
These define the model’s '''slope and relationship''' between experience and income.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''y_pred_train = lr.predict(x_train) '''&lt;br /&gt;
&lt;br /&gt;
'''y_pred_train = y_pred_train.round().astype(int) '''&lt;br /&gt;
&lt;br /&gt;
'''y_pred_train '''&lt;br /&gt;
|| Now, we use the trained model to make '''predictions on the training data.'''&lt;br /&gt;
&lt;br /&gt;
We round the predictions to whole numbers for better readability.&lt;br /&gt;
&lt;br /&gt;
Then, we display the rounded predictions.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''mae_train = mean_absolute_error(y_train, y_pred_train) '''&lt;br /&gt;
&lt;br /&gt;
'''print(&amp;quot;MAE (Training):&amp;quot;, mae_train)'''&lt;br /&gt;
&lt;br /&gt;
|| Next, we calculate the '''Mean Absolute Error''' on the training data.&lt;br /&gt;
&lt;br /&gt;
'''Mean Absolute Error''' measures '''prediction accuracy.'''&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Highlight the lines:&lt;br /&gt;
&lt;br /&gt;
'''r2_score(y_pred_train, y_train) '''&lt;br /&gt;
|| Then, we compute the '''R squared score''' to evaluate the model’s performance.&lt;br /&gt;
&lt;br /&gt;
'''R squared score''' measures how well the model explains the '''variance''' in the data.&lt;br /&gt;
&lt;br /&gt;
A '''value closer to''' '''1''' indicates a '''stronger fit.'''&lt;br /&gt;
&lt;br /&gt;
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'''y_pred_test = lr.predict(x_test) '''&lt;br /&gt;
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'''y_pred_test = y_pred_test.round().astype(int) '''&lt;br /&gt;
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'''y_pred_test '''&lt;br /&gt;
&lt;br /&gt;
|| Now, we make predictions on the test data.&lt;br /&gt;
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'''plt.scatter(x_test,y_test) '''&lt;br /&gt;
&lt;br /&gt;
|| To visualize performance, we create a '''scatter plot of actual vs predicted values'''.&lt;br /&gt;
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|| Show the output&lt;br /&gt;
|| In the output we can see that most points are close to the line.&lt;br /&gt;
&lt;br /&gt;
It shows a '''positive correlation.'''&lt;br /&gt;
&lt;br /&gt;
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'''mean_absolute_error(y_test,y_pred_test) '''&lt;br /&gt;
&lt;br /&gt;
|| Now, compute the '''Mean Absolute Error '''on the test data.&lt;br /&gt;
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'''r2_score(y_pred_test, y_test) '''&lt;br /&gt;
|| Then, we calculate and display the '''R squared score'''.&lt;br /&gt;
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|| Narration&lt;br /&gt;
&lt;br /&gt;
|| The model has a '''Mean Absolute Error of 1626.41''', indicating prediction errors.&lt;br /&gt;
&lt;br /&gt;
The '''R-squared score of 0.87''' shows the model explains most of the variance.&lt;br /&gt;
&lt;br /&gt;
Overall, the model performs well but has some prediction errors.&lt;br /&gt;
&lt;br /&gt;
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|| &lt;br /&gt;
|| Now let us see the implementation of '''Multiple Linear Regression'''.&lt;br /&gt;
&lt;br /&gt;
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'''df_salaries = pd.read_csv(r&amp;quot;salaries_mlr.csv&amp;quot;) '''&lt;br /&gt;
&lt;br /&gt;
|| First, load the dataset for '''Multiple Linear Regression'''.&lt;br /&gt;
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'''df_salaries.tail()'''&lt;br /&gt;
&lt;br /&gt;
|| Then, we display the '''last five rows.'''&lt;br /&gt;
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'''df_salaries.dtypes'''&lt;br /&gt;
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|| Next, we check the '''data types''' of each column in the dataset.&lt;br /&gt;
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'''df_salaries.isnull().sum()'''&lt;br /&gt;
|| We also check for any '''missing values''' in the dataset by summing them.&lt;br /&gt;
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'''df_salaries['gender'] = df_salaries['gender'].map({'m': 1, 'f': 0}) '''&lt;br /&gt;
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|| Now, we convert '''gender column''' to numeric values, '''1 for Male''' and '''0 for Female'''.&lt;br /&gt;
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'''X = df_salaries.drop(columns='income')'''&lt;br /&gt;
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'''y = df_salaries['income']'''&lt;br /&gt;
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|| Then, we separate the '''features X''' and the '''target variable y''' for prediction.&lt;br /&gt;
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'''X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42) '''&lt;br /&gt;
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|| Now, we split the data into '''training and testing sets.'''&lt;br /&gt;
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'''model = LinearRegression()'''&lt;br /&gt;
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'''model.fit(X_train, y_train)'''&lt;br /&gt;
&lt;br /&gt;
|| We initialize a''' Linear Regression model''' and train it using the training data.&lt;br /&gt;
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'''coefficients = pd.DataFrame({'Feature': X.columns, 'Coefficient': model.coef_}) '''&lt;br /&gt;
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|| Next, we print the model's '''coefficients and intercept'''. &lt;br /&gt;
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'''y_train_pred = model.predict(X_train) '''&lt;br /&gt;
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'''y_train_pred = y_train_pred.round().astype(int) '''&lt;br /&gt;
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'''y_train_pred'''&lt;br /&gt;
|| Now, we make '''predictions on the training data.'''&lt;br /&gt;
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'''mae_train = mean_absolute_error(y_train, y_train_pred) print(f'Training data MAE: {mae_train}') '''&lt;br /&gt;
&lt;br /&gt;
|| Next, we compute the '''Mean Absolute Error for training data'''.&lt;br /&gt;
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'''r2_train = r2_score(y_train, y_train_pred) '''&lt;br /&gt;
&lt;br /&gt;
'''n_train = len(y_train'''&lt;br /&gt;
|| Then, we computethe '''R squared score''' to measure the model performance&lt;br /&gt;
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After that, we compute and print the '''adjusted R squared '''score.&lt;br /&gt;
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'''y_test_pred = model.predict(X_test) '''&lt;br /&gt;
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'''y_test_pred = y_test_pred.round().astype(int) '''&lt;br /&gt;
&lt;br /&gt;
|| Moving forward, we make '''predictions on the test data.'''&lt;br /&gt;
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'''plt.scatter(y_test, y_test_pred, color='red', label='Predicted') '''&lt;br /&gt;
&lt;br /&gt;
'''plt.scatter(y_test, y_test, color='blue', alpha=0.5, label='Actual') '''&lt;br /&gt;
|| We compare '''actual vs predicted income''' using a '''scatter plot.'''&lt;br /&gt;
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'''mae_test = mean_absolute_error(y_test, y_test_pred) print(f'Testing data MAE: {mae_test}')'''&lt;br /&gt;
&lt;br /&gt;
|| Then, we compute the '''Mean Absolute Error''' for the test data.&lt;br /&gt;
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'''r2_test = r2_score(y_test, y_test_pred) '''&lt;br /&gt;
&lt;br /&gt;
'''n_test = len(y_test) '''&lt;br /&gt;
&lt;br /&gt;
'''k_test = X_test.shape[1] '''&lt;br /&gt;
|| Next, we calculate the '''R squared score '''for the test data.&lt;br /&gt;
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|| Narration&lt;br /&gt;
|| The model has an '''MAE''' of '''1700.15''', showing the average prediction error in income.The '''Adjusted R squared score''' is '''0.921'''.&lt;br /&gt;
&lt;br /&gt;
It indicates the model explains '''92.1 percent''' of income variance.&lt;br /&gt;
&lt;br /&gt;
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'''residuals = y_test - y_test_pred '''&lt;br /&gt;
&lt;br /&gt;
'''plt.show()'''&lt;br /&gt;
&lt;br /&gt;
|| Now, we analyse the '''residuals''' to check model errors.&lt;br /&gt;
&lt;br /&gt;
We create a '''scatter plot''' of '''predicted values versus residuals.'''&lt;br /&gt;
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|| Highlight the output&lt;br /&gt;
&lt;br /&gt;
|| This is a '''residual plot''' for the regression model.&lt;br /&gt;
&lt;br /&gt;
The '''red dashed line''' represents '''zero residual.'''&lt;br /&gt;
&lt;br /&gt;
Points above the line mean predictions are lower than actual values.&lt;br /&gt;
&lt;br /&gt;
Points below the line mean predictions are higher than actual values.&lt;br /&gt;
&lt;br /&gt;
Most '''residuals''' are '''close to zero''', meaning predictions are fairly accurate.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Narration&lt;br /&gt;
|| Thus, we successfully implemented '''Multiple Linear Regression'''.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show slide:&lt;br /&gt;
&lt;br /&gt;
'''Summary'''&lt;br /&gt;
|| This brings us to the end of the tutorial. Let us summarize.&lt;br /&gt;
&lt;br /&gt;
In this tutorial, we have learnt about&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;'''Linear Regression'''&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;'''Simple Linear Regression'''&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;'''Multiple Linear Regression'''&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''Evaluation Metrics'''&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide:&lt;br /&gt;
&lt;br /&gt;
'''Assignment'''&lt;br /&gt;
&lt;br /&gt;
In Multiple Linear Regression code,&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;Replace the test_size parameter as shown here.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
|| In Multiple Linear Regression code, &lt;br /&gt;
&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;R&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;eplace the &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''test_size parameter'''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt; as shown here.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
* &amp;lt;div style=&amp;quot;margin-left:1.27cm;margin-right:0cm;&amp;quot;&amp;gt;Ob&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;serve the change in &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''MAE '''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;and &amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;'''Adjusted R squared score'''&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:transparent;color:#000000;&amp;quot;&amp;gt;.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div style=&amp;quot;color:#000000;&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide:&lt;br /&gt;
&lt;br /&gt;
'''Assignment Solution'''&lt;br /&gt;
&lt;br /&gt;
Show s1 img file&lt;br /&gt;
|| After completing the assignment, the output should match the expected result.&lt;br /&gt;
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|| Show Slide:&lt;br /&gt;
&lt;br /&gt;
'''FOSSEE Forum'''&lt;br /&gt;
|| For any general or technical questions on &amp;lt;span style=&amp;quot;background-color:#ffffff;&amp;quot;&amp;gt;'''Python&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;background-color:#ffffff;&amp;quot;&amp;gt; for Machine Learning'''&amp;lt;/span&amp;gt;, visit the''' FOSSEE forum''' and post your question.&lt;br /&gt;
&lt;br /&gt;
|- style=&amp;quot;border:0.5pt solid #000000;padding-top:0cm;padding-bottom:0cm;padding-left:0.191cm;padding-right:0.191cm;&amp;quot;&lt;br /&gt;
|| Show Slide: &lt;br /&gt;
&lt;br /&gt;
'''Thank you'''&lt;br /&gt;
|| &amp;lt;div style=&amp;quot;color:#000000;&amp;quot;&amp;gt;This is '''Harini Theiveegan''', a FOSSEE Summer Fellow 2025, IIT Bombay signing off&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Thanks for joining.&lt;br /&gt;
&lt;br /&gt;
|-&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Nirmala Venkat</name></author>	</entry>

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