A real estate expert was interested in developing a regression model that relates the selling
price (in thousand of dollars) of properties to characteristics of the properties. Data were
available on 30 properties that were sold recently. The expert developed a long list of possible
explanatory variables. After a careful screening, it was decided that the following four
characteristics should be considered.
x1 Property taxes (annual taxes in dollars)
x2 House size (floor area in square feet)
x3 Lot size (in acres)
x4 Attractiveness Index
Regression Analysis: Selling Price versus Taxes, House, Lot, Attract
The regression equation is
Selling Price = 11.8 - 0.0233 Taxes + 0.109 House + 44.4 Lot + 2.99 Attract
Predictor Coef SE Coef T P
Constant 11.83 66.32 0.18 0.860
Taxes -0.02331 0.02056 -1.13 0.268
House 0.10948 0.02442 4.48 0.000
Lot 44.40 21.76 2.04 0.052
Attract 2.9926 0.6589 4.54 0.000
S = 32.13 R-Sq = 72.1% R-Sq(adj) = 67.7%
Analysis of Variance
Source DF SS MS F P
Regression 4 66827 16707 16.18 0.000
Residual Error 25 25815 1033
Total 29 92641
(a) Write out the GENERAL MLR model for this problem.(no numbers just Letters: Beta
β0,, β1… and X1 , X2….)
(b) Write out the estimated (least-squares) regression line for this problem.
(c) Use the estimated regression line to predict the average selling price of 2900 square-
foot homes on a 2.5-acre lot with $6000 in annual property taxes and an attractive
index of 45.
(d) Interpret the b3 slope estimate in terms of this problem.
(e) If you Calculate the 95% confidence interval for 2 as shown below
(f) What is the correlation coefficient?
(g) What percentage of variation in selling price is explained by the multiple linear
regression model using taxes, house size, lot size, and attractiveness as predictors?