STAT 440 - Forecasting
Class Activity - Partitioning Sums of Squares
(counts as Lecture Review #12)

Computational exercises:

Work these problems on a spreadsheet or other computational tool.

Consider the following three data sets:

1) For Data Set #1:

a) Find the intercept and slopes for the multiple regression line for the data.

b) Find the sums of squares (regression, error, total) for the regression line.

c) Now, find the sum of squares for regression (SSR) for the simple regression model which uses only “Sleep” as a predictor variable.

d) Also, find the sum of squares for regression (SSR) for the simple regression model which uses only “Skip” as a predictor variable.

e) What is the relationship between the Sums of Squares for Regression, from parts “b”, “c”, and “d”?

2) Now repeat the process, for Data Set #2.

3) And again, for Data Set #3.

Discussion question:

NOTE that the "Sleep" data are the same in each data set. Likewise, the "Skip" data are the same in each data set. All that is changed is the connection between which "Sleep" number went with which "Skip" number. Likewise, the regression model is the same for each data set. (Intercept = 46, slopes of 7 and -5.)

WHY are your results on the Sums of Squares different for the three data sets?

Also: WHY are the slopes affected in Data Sets #2 and #3, but not in #1?