Question 1:

There has been a lot of discussion regarding the relationship between Scholastic Aptitude Test (SAT) scores and test-takers' family income (New York Times, August 27, 2009). It is generally believed that the wealthier a student's family, the higher the SAT score. Another commonly used predictor for SAT scores is the student's grade point average (GPA). Consider the following data collected on 24 students. The data can also be found on the text website, labeled SAT.

1. Estimate three models:

1. \(S A T=\beta_{0}+\beta_{1}\) lncome \(+\varepsilon_{r}\)
2. \(\mathrm{SAT}=\beta_{0}+\beta_{1} \mathrm{GPA}+\varepsilon\), and
3. \(\mathrm{SAT}=\beta_{0}+\beta_{1}\) Income \(+\beta_{2} \mathrm{GPA}+\varepsilon\).

b. Use goodness-of-fit measures to select the best-fitting model.

c. Predict SAT given the mean value of the explanatory variable(s).

Question 2 :

FILE A researcher interviews 50 employees of a large manufacturer and collects data on each worker's hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE). The data can be found on the text website, labeled Hourly Wage.

1. Estimate: Wage \(=\beta_{0}+\beta_{1} \mathrm{EDUC}+\beta_{2} \mathrm{EXPER}+\beta_{3} \mathrm{AGE}+\varepsilon\).
2. Are the signs as expected?
3. Interpret the coefficient of EDUC.
4. Interpret the coefficient of determination.
5. Predict the hourly wage of a 40 -year-old employee who has 5 years of higher education and 8 years of experience.

Question 3:

Megan Hanson, a realtor in Brownsburg, Indiana, would like to use estimates from a multiple regression model to help prospective sellers determine a reasonable asking price for their homes. She believes that the following four factors influence the asking price (Price) of a house: (1) the square footage of the house (SQFT); (2) the number of bedrooms (Bed); (3) the number of bathrooms (Bath); and (4) the lot size (LTSZ) in acres. She randomly collects online listings for 50 single-family homes. A portion of the data is presented in the accompanying table; the complete data can be found on the text website, labeled Indiana Real Estate.

Data for Case Study 14.3 Real Estate Data for Brownsburg, Indiana

In a report, use the sample information to:

1. Provide summary statistics on the asking price, square footage, the number of bedrooms, the number of bathrooms, and the lot size.
2. Estimate and interpret a multiple regression model where the asking price is the response variable and the above four factors are the explanatory variables.
3. Interpret the resulting coefficient of determination.

Price: $14.64

Solution: The downloadable solution consists of 6 pages, 864 words and 8 charts.
Deliverable: Word Document