STAT 440 - Forecasting
Lecture Review #10 - Multiple Regression

Review questions:

1) What is multiple regression analysis? When is it used?

Computational exercise:

Real estate appraisers rely heavily on multiple regression analysis in their evaluation of property. Typically, the sale price of a home is modeled as a function of several home-related variables (such as home size, home condition, location, etc.).

Given below are data on ten homes, including the sale price (in thousands of dollars), home size (hundreds of square feet), and a rating of the house's condition (1=low, 10=high). (The data are taken from a 1986 issue of a professional journal, The Real Estate Appraiser and Analyst.) They're supposedly real data, but a tad dated — hence the low housing values.)

Perform a multiple regression analysis on these data. (Use Excel.) Interpret the output. In particular:

a) What is r² for these data? What does this number mean?

b) Give the regression model for the data. Interpret the coefficients.

c) Do home size and condition appear to be meaningful predictors of house price? Explain.

SOLUTIONS:

a) r² = .990, i.e., 99% of the variation in housing sale price is explained by these two variables. (Aside: I'm inclined to think these are fake data — in the real world you don't get that good of a result. I don't have the original journal, just a statistics textbook that used these data for a homework problem.)

b) Y = 9.78 + 1.87*HomeSize + 1.28*Condition
Each 100 sq. ft. of home size adds 1.87 $K (i.e., $1870) to home price, on avg., AABE.
Each "condition point" adds $1280 to home price, on avg. AABE.
Base home price is $9780. (They aren't free.)

c) Both predictors are highly significant — t scores of 24.56 and 8.85, respectively.