Objective Introduction Plotting Prediction Examples
The Regression module targets the following cognitive tasks:
| Task Skills | Concepts | |
|---|---|---|
| Regn-1: | Compute the intercept and slope of a straight line | Understand the general form of a straight line |
| Regn-2: | Use least squares to estimate the intercept ( |
Understand the idea of least squares estimation |
| Regn-3: | Interpret the intercept and slope of a least square line | |
| Regn-4: | Compute pedicted values | Understand predicted values |
| Regn-5: | Compute the residuals | Understand the diagnostic value of residuals |
| Regn-6: | Construct a confidence interval for the mean of |
Understand the form of a confidence interval for the mean of |
| Regn-7: | Construct a confidence interval for a single predicted value | Understand the form of a confidence interval for a single predicted value |
| Regn-8: | Construct a confidence interval on |
Understand the form of a confidence interval on |
| Regn-9: | Perform a hypothesis test on |
Understand why the test on |
| Regn-10: | Interpret the results of the test on |
|
| Regn-11: | Understand the connection between correlation and regression analysis |
The regression line can be used to predict the value of y for a given value of x. Predictions should be made within the range of the x values and (generally) should not be made beyond this range, i.e., the regression equation should not be extrapolated (extended) beyond the range of the x values.
In the above applet, select Regression from the Model menu and then select 95% confidence limits from the Options menu. Drag the vertical line, representing a 95% confidence interval on the mean, to get predicted y values for a range of x values.
Example #1 (GB Tobacco/Alcohol Spending)
Example #4 Advertising Expenses Self-test