Applications-of-GeoGebra/C3/Statistics-using-GeoGebra/English-timed

Time	Narration
00:01	Welcome to this tutorial on Statistics using GeoGebra.
00:06	In this tutorial, we will learn how to use GeoGebra to perform:
00:12	One Variable Analysis to calculate different statistical parameters.
00:18	Two Variable Regression Analysis to estimate best fit line.
00:23	Multiple Variable Analysis to calculate different statistical parameters.
00:29	Here I am using: Ubuntu Linux Operating System version 16.04.
00:36	GeoGebra 5.0.481.0 hyphen d.
00:43	To follow this tutorial, you should be familiar with: GeoGebra interface, Statistics
00:51	Statistics deals with Data analysis and interpretation.
00:56	Measures of central tendency.
00:59	Measures of Dispersion.
01:02	Comparing variability of data series.
01:06	Please refer to additional material provided along with this tutorial.
01:12	Fish Feed
01:14	Let us look at an example.
01:17	A fishery is testing four types of feed formulations on its fish: A, B, C and D.
01:26	Data to be collected after feeding the fish for 6 months are: Length in millimeters, Weight in pounds, Girth in millimeters.
01:39	Let us look at some of these data.
01:42	Fish Feed Data
01:44	We will use these data for our analyses.
01:49	Please download the code file, Fishery-data, provided along with this tutorial.
01:57	I have opened the GeoGebra interface.
02:01	Click on View tool and select Spreadsheet.
02:07	Click on X at top right corner of Graphics and Algebra views. This will close these views.
02:17	In the code file, drag mouse to highlight length and weight data from columns H and I.
02:26	These are data for fish that have been fed formulation C.
02:32	Hold Control key down and press C.
02:36	Click in the top of the Spreadsheet in GeoGebra.
02:41	Hold Control key down and press V.
02:45	This will copy and paste the highlighted data from the code file into GeoGebra.
02:52	Place the cursor on the first column header in Spreadsheet view.
02:58	Drag and adjust column A's width.
03:02	Right-click on column A heading of Length millimetres.
03:08	Select Object Properties.
03:11	A dialog box opens.
03:14	Click on Text tab and change the name to Length millimetres hyphen C.
03:23	Close the dialog box.
03:26	Similarly, add hyphen C to Weight pounds.
03:35	Adjust column B width.
03:38	Click on column A heading of Length millimetres C.
03:44	Drag to highlight length data in Spreadsheet view.
03:49	Below the menubar, click on One Variable Analysis tool.
03:55	A Data Source popup window appears. Click on Analyze button.
04:02	A Data Analysis window appears.
04:06	By default, a histogram is plotted.
04:10	Drag the boundary to see the graph properly.
04:14	The length is plotted on the x-axis.
04:18	The number of fish that are of a particular length, the frequency, is plotted on the y-axis.
04:26	Note the display box above the graph containing the word Histogram.
04:32	In the display box, click on the dropdown menu button to display the list of plots.
04:39	We will stay with the histogram option.
04:43	To the right of the dropdown menu is a slider.
04:48	Drag the slider from left to right to go to 20.
04:53	The slider changes the number of rectangles between the minimum and maximum values of data.
05:01	Click on Options button to the right of the slider.
05:06	Under Classes, check Set Classes Manually check box.
05:12	This displays Start and Width text-boxes to the left of the Options button.
05:19	As all the fish are over 800 milimeters long, type 800 in the Start text-box and press Enter.
05:29	We will stay with the default value of 5 for rectangle width.
05:35	Uncheck Set Classes Manually check box.
05:39	Under Show, uncheck Histogram check box to make it disappear.
05:45	Scroll down and check Frequency Polygon to show it.
05:51	Under Frequency Type, check Cumulative option.
05:56	The default Count selection shows the cumulative frequency count for the data.
06:03	Drag the slider and note the effects on smoothness of the cumulative frequency count curve.
06:11	We will drag the slider back to 20.
06:15	Under Frequency Type, uncheck Cumulative and under Show, uncheck Frequency Polygon.
06:24	Under Show, check Histogram . And click on Options button again to hide the window.
06:33	Above the Histogram text-box, click on the third Show Data tool button.
06:40	This displays all the data highlighted in the Spreadsheet.
06:45	Drag the boundary to see the data properly.
06:49	Click on the Show Data tool again to hide the list.
06:55	Above the Histogram text-box, click on the last Show 2nd Plot tool button.
07:02	The same data are graphed in two vertically placed plots.
07:07	You can select plot types from the dropdown menu button above each plot.
07:14	Above the Histogram text box, click on the second Show Statistics tool button.
07:22	Statistics for the plot appears as a panel in the middle.
07:27	Drag the boundary to see it properly.
07:31	Box Plot Box plot is a standardized way of showing data, based on the five number summary.
07:41	Let us compare histogram and box plot.
07:45	In the box plot, locate the Median, Min, Max, Q1 and Q3 values.
07:57	Above each plot, in the upper right corner, click on the button next to Options.
08:06	A dropdown menu appears with which you can copy each plot to Clipboard or export it as an image.
08:15	Click on Show Statistics tool button to hide the data.
08:21	Close the Data Analysis window.
08:25	Least Squares Linear Regression (LSLR)
08:30	Changing an independent variable x changes the dependent variable y.
08:36	LSLR predicts y based on x value.
08:41	Least Squares Regression Line (LSRL) is also called the best fit line.
08:49	It is given by y = b0 + b1x.
08:55	b1, the slope, is the regression coefficient.
09:00	Coefficient of determination R squared
09:04	R squared ranges from 0 to 1.
09:08	The closer R squared is to 1, the better is the prediction of variance in y from x.
09:16	Let us go back to the length and weight data in the Spreadsheet view in GeoGebra.
09:23	Drag and select all the data in both columns.
09:29	Under One Variable Analysis, click on Two Variable Regression Analysis tool.
09:36	In the Data Source window that pops up, click Analyze button.
09:41	A Data Analysis window appears with two plots.
09:46	By default, the upper plot is a Scatterplot and the lower a Residual plot.
09:54	Click on Show Statistics tool to see the Statistics.
10:00	Drag the boundary to see them properly.
10:04	Below the Statistics window, click on the Regression Model menu button and select Linear.
10:13	Note the red line in the Scatterplot.
10:17	This is the best fit line that passes through as many points as possible.
10:23	Its equation is given in red at the bottom.
10:28	This R squared value indicates good fit between the model and the actual data.
10:36	Select other regression models to see effects on the R squared value.
10:43	The lower plot is the Residual Plot.
10:47	Residuals are the differences between observed and predicted values of all points.
10:54	Above the Statistics window, click on the last Switch Axes button.
11:00	For the scatterplot, length is now plotted along y axis and weight along x axis.
11:08	Observe that the best fit line and many statistics change.
11:13	Its equation is now y= 9.91x + 684.3.
11:22	The only statistics that remain the same are r, R squared and rho (ρ).
11:31	Note that r and rho are greater than 0.8, indicating positive correlation.
11:39	Weight increases as length increases for fish given feed C.
11:46	The relationship is strong and well predicted by the best fit lines.
11:52	Again, click on Switch Axes button.
11:56	At the bottom, in Symbolic Evaluation, you can enter a value for x to get a prediction for y.
12:04	To get logical predictions, we will enter x values above the x intercept.
12:11	In Symbolic Evaluation, in the text-box for x, type 800 and press Enter.
12:19	Note that a y value appears next to the display box.
12:25	The x value was substituted in the best fit line equation to get the y value.
12:32	Again, click on Show Statistics tool button.
12:37	Close the Data Analysis window.
12:40	Let’s go back to the length and weight data in the Spreadsheet.
12:45	In the Spreadsheet, select all the data in both columns.
12:51	Under One Variable Analysis, click on Multiple Variable Analysis tool.
12:59	In the Data Source window that pops up, click Analyze button.
13:04	Box Plots appear in the window.
13:07	They are for length and weight data.
13:11	Above the plot, click on the second Show Statistics tool.
13:17	Statistics for both plots appear below.
13:21	Place the cursor on the boundary between the plot and statistics.
13:27	When the arrow appears, drag the boundary to resize the windows.
13:34	Let us summarize.
13:36	In this tutorial, we have learnt how to use GeoGebra to perform:
13:41	One Variable Analysis to calculate different statistical parameters.
13:47	Two Variable Regression Analysis to estimate best fit line.
13:52	Multiple Variable Analysis to calculate different statistical parameters.
13:58	Assignment Perform statistical analyses for weight and girth data given in this tutorial.
14:07	Four oils were used to deep fry chips.
14:11	Amount of absorbed fat was measured for 6 chips fried in 4 oils.
14:19	Is any of the oils absorbed more than the others?
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