Interpreting multiple regression output tables

This multiple regression equation was estimated using 2005 data for 100 homes in Plano, Texas: $\mathrm{Y}=15.034+104.96 \mathrm{~ S}+56.68 \mathrm{G}-12,018 \mathrm{~ A}-5,225 \mathrm{BR}+3,396 \mathrm{BA}+23,835 \mathrm{AC}, \mathrm{R}^{2}=.774 \begin{array}{llllll}(2.206) & (11.70) & (13.70) & (793) & (2,187) & (1,235)\end{array}(4,793)$ where: $\mathrm{Y}=$ home price $\mathrm{S}=$ square feet of living area G = garage square feet A = age of house in years BR = number of bedrooms BA = number of bathrooms $\mathrm{AC}=1$ if it has central air, 0 if not and standard errors are in parentheses.

A student estimated a regression model that used the number of pages in best-selling hardcover books to predict their prices. Explain why this conclusion is wrong: "The 0.75 R-squared is pretty large, when you consider that the price of a book is $\$ 20$ and $.75(\$ 20)=\$ 15$ of the price is explained by the number of pages."

The following multiple regression model was used to explain the sale prices (in thousands of dollars) for 60 single-family homes in Oxnard, California:

A study of home prices in a suburban Rhode Island town used these variables in a multiple regression model: $\mathrm{Y}=$ price $\mathrm{X}_{1}=$ square feet $\mathrm{X}_{2}=$ number of bedrooms $\mathrm{X}_{3}=$ number of bathrooms $\mathrm{X}_{4}=$ Walk Score, a rating (from 0 to 100) for a given address, based on the walking distance from that address to a variety of key amenities. A Walk Score of 70 or above is generally considered good.

What is wrong with this interpretation of the results: "The coefficient of $\mathrm{X}_{4}$ is negative because large homes that have high prices are usually secluded from grocery stores, coffee shops, and other desirable destinations."

Identify two ways in which this report of the estimation of a multiple regression equation could be improved:

How would you respond to this question?

I have run into a problem with missing values in my data. Some of the variables including GPA and parents' education have a lot of missing values. If I discard those individuals with missing values, then the dataset becomes very small, but if I replace all the missing values with zeros, the total sample size is about 35,000 and I am able to get statistically significant results.

A multiple regression model was used to estimate the relationship between a Major League Baseball (MLB) player's salary and his batting average and home runs:

Can we conclude from these results that salaries are affected more by batting average than by home runs, or vice versa? Explain your reasoning.

Data for the top 100 money winners on the 1993 Professional Golf Association (PGA) tour were used to estimate the following equation: $\mathrm{Y}=-8,023,111+15,992 \mathrm{D}+12,003 \mathrm{~ A}+27,003 \mathrm{G}+91,306 \mathrm{P}+11,357 \mathrm{~ S}$

where: Y = dollars won D = average length of drives from the tee, yards A = driving accuracy (percent of drives landing in fairway) G = percent of greens that were reached in par minus two strokes $\mathrm{P}=$ percent of those greens reached in par minus two that required only one putt $\mathrm{S}=$ percent of times player made par after hitting into sand The standard errors are in parentheses; the t -values are in brackets; and $\mathrm{R}^{2}=.468$.

Do you agree or disagree with the following statements?