Question: Lets return to the height-weight example on page 53 and recall what happened when we added a nonsensical variable that measured the students campus post

Let’s return to the height-weight example on page 53 and recall what happened when we added a nonsensical variable that measured the student’s campus post office box number (MAIL) to the equation. The estimated equation changed from:

To:

a. The estimated coefficient of HEIGHT changed when we added MAIL to the equation. Does that make sense? Why?

b. In theory, someone’s weight has nothing to do with their campus mail box number, yet R² went up from .74 to .75 when MAIL was added to the equation! How is it possible that adding a nonsensical variable to an equation can increase R²?

c. Adding the nonsensical variable to the equation decreased R² from .73 to .72. Explain how it’s possible that R² can go down at the same time that R² goes up.

d. If a person’s campus mail box number truly is unrelated to their weight, shouldn’t the estimated coefficient of that variable equal exactly 0.00? How is it possible for a nonsensical variable to get a nonzero estimated coefficient?

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