In Exercise 15.16 the adjusted R2 would actually be lower for five predictors than for three predictors. Why? The State of Vermont is divided into 10 Health Planning Districts—they correspond roughly...

In Exercise 15.16 the adjusted R2 would actually be lower for five predictors than for three predictors. Why?

The State of Vermont is divided into 10 Health Planning Districts—they correspond roughly to counties. The following data represent the percentage of live births of babies weighing under 2500 grams (Y), the fertility rate for females 17 years of age or younger (X₁), total high-risk fertility rate for females younger than 17 or older than 35 years of age (X₂), percentage of mothers with fewer than 12 years of education (X₃), percentage of births to unmarried mothers (X₄), and percentage of mothers not seeking medical care until the third trimester (X₅).

A stepwise regression is shown in Exhibit 15.7. (Only the first three steps are shown to conserve space. For purposes of this exercise, we will not let the lack of statistical significance worry us.)

a. What are the values of R for the successive steps?

b. From the definition of a partial correlation (in terms of Venn diagrams), show that the R2 at step 2 is a function of R2 at step 1 and the partial correlation listed under