Explanation Since the location is a categorical variable with two categories â€œGlen coveâ€� and â€œRoslynâ€�. Therefore, add a dummy variable which takes value 1 if the location is â€œGlen coveâ€� and 0 if the location is â€œRoslynâ€�. Model without interaction terms: Software procedure: Open the â€œ GCRoslyn â€� workbook. Add a dummy variable Glen Cove in C10. Select the Stat > Regression > Regression > Fit regression model . Double click on column C3 to add â€œ Fair market value â€� column to Reponses box. Double click on column C4, C5 and C10 to add â€œ Property size â€�, â€œ Age â€� and â€œ Glen Clove â€� to Continuous predictors box. Click Ok. The Minitab output shows that the multiple regression equation is, fair market value = − 99.1 + 527.1 Property size + 0.2843 Age + 411.4 Glen Clove . Model with i n teraction terms : Software procedure: In the opened workbook, Select the Stat > Regression > Regression > Fit regression model . Double click on column C3 to add â€œ Fair market value â€� column to Reponses box. Double click on column C4, C5 and C10 to add â€œ Property size â€�, â€œ Age â€� and â€œ Glen Clove â€� to Continuous predictors box. Click Models , in Model dialog box, click â€˜ Property size â€™ in predictors list. While holding ctrl key, click â€œ Age â€� in the predictors list. Click Add that is to the right of interactions through order. Then , click â€˜ Property size â€™ in predictors list. While holding ctrl key, click â€œ Glen Clove â€� in the predictors list. Click Add that is right of interactions through order. Then , click â€˜ Age â€™ in predictors list. While holding ctrl key, click â€œ Glen Clove â€� in the predictors list. Click Add that is right of interactions through order. Click OK in each box. The Minitab output shows that the multiple regression equation is, fair market value = 115 + 128 Property Size + 0.1354 Age + 423 Glen Cove +0 .385 Property Size × Age +256Property Size × Glen Cove − 3.051 Age × Glen Cove Testing the significance of model with interaction Step 1: Consider β 4 , β 5 , β 6 are the coefficients of the interaction term between â€œProperty size & Age, Property size & Glen Clove and Age & Glen Cloveâ€�. Null and alternative hypothesis are given below: H 0 : β 4 = β 5 = β 6 H 1 : At least one is different from zero Step 2: The level of significance is 5 % . Step 3: The Minitab output shows that the S S R X 1 , X 2 , X 3 , X 4 , X 5 , X 6 = 3961302 , S S R X 1 , X 2 , X 3 = 3672105 and M S E X 1 , X 2 , X 3 , X 4 , X 5 , X 6 = 7233 . Therefore, the test statistic is calculated below: F S T A T = S S R X 1 , X 2 , X 3 , X 4 , X 5 , X 6 − S S R X 1 , X 2 , X 3 3 M S E X 1 , X 2 , X 3 , X 4 , X 5 , X 6 = 3961302 − 3672105 3 7233 = 96399 7233 = 13.328 Step 4: The critical value at 3 degrees of freedom in numerator and 53 degrees of freedom in denominator corresponding to cumulative probability of 97

Basic Business Statistics, Student Value Edition

14th Edition

ISBN: 9780134685113

Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat

Publisher: PEARSON

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Chapter 14, Problem 79PS

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Find the appropriate multiple regression model to predict fair market value based on the land area of a property, the age of a house and location. Also, test whether the interaction terms should be included in the model.

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Chapter 14, Problem 78PS

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Basic Business Statistics, Student Value Edition

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Find the appropriate multiple regression model to predict fair market value based on the land area of a property, the age of a house and location. Also, test whether the interaction terms should be included in the model.

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Find the appropriate multiple regression model to predict fair market value based on the land area of a property, the age of a house and location. Also, test whether the interaction terms should be included in the model.

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