# MTH Multiple Linear Regression Questions

**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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