MTH Multiple Linear Regression Questions

timer Asked: Jun 24th, 2015

Question description

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.

Variable Description 

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?

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