Answers for Module 1, Exercise 2:

Module 1, Exercise 2a:

Look at the plot of the data. Does it appear that the regression model will explain a large portion of the variance in Y?

The plot does not show a clear relationship between values of X and Y. Thus, we do not expect that a linear regression model will account for much of the variance in Y.

Module 1, Exercise 2b:

Add your calculated values for each column to check against the sum that is shown in the table. If you get a different answer, check your calculations for the first row to make sure that you used the right values. Then use the same procedure for each of the remaining rows. Here are answers for the second case.

Module 1, Exercise 2c:

The largest deviation from the mean is -1.25 for Case 3.

Module 1, Exercise 2d:

The ratio of the contribution to the SS total for Case 3 compared to Case 2 is 1.5625:.0625, which simplifies to 25:1. Notice that the deviation from the mean is five times greater for Case 3 compared to Case 2 (-1.25 vs. -.25), so the squared contribution is 25 times greater.

Module 1, Exercise 2e:

The largest deviation from the mean is -1.20 for Case 3.

Module 1, Exercise 2f:

The red boxes for SS Error are very similar to the black boxes for SS Total, so it appears that SS Error is nearly as large as SS Total. The computed values confirm this conclusion. SS Error = 2.70, while SS Total = 2.75.

Module 1, Exercise 2g:

The red boxes for SS Predicted are much smaller than the black boxes for SS Total, so it appears that SS Predicted is only a small fraction of SS Total. The computed values confirm this conclusion. SS Predicted = .05, while SS Total = 2.75.

Module 1, Exercise 2h:

SS Total = 2.75

SS Predicted = .05

SS Error = 2.70

SS Total          =  SS Predicted   +  SS Error

2.75 = .05 + 2.70

Module 1, Exercise 2i:

[SS Predicted / SS Total] = [.05_ / 2.75]  = .018

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