Write out the general Multiple linear regression model for this problem with

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Multiple Linear Regression Worksheet

• Answer All questions • Work Independently

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 Multiple linear regression model for this problem with

(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) What is the b3 slope estimate in terms of this problem?

(e) What is the correlation coefficient determined by the multiple linear regression model using taxes, house size, lot size, and attractiveness as predictors?

(f) 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?

(g) State your decision regarding the null hypothesis about the slope b3 in (d). (Use = 0.05) (Accept or reject Ho) Explain

(h) If we Calculate the 95% confidence interval for and got the following :

How would you interpret the C.I. in part (h) in terms of the problem?

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