A real estate builder wishes to determine if family income (in thousands of dollars) and family size can help predict the size of house (in hundreds of square feet) a person buys. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics egin{tabular}{|l|l|} hline Multiple R & 0.8479 \ hline R Square & 0.7189 \ hline Adjusted R Square & 0.7069 \ hline Standard Error & 0.299 \ hline Observations & 50 \ hline end{tabular} egin{tabular}{|l|l|l|c|c|} hline & multicolumn{1}{|c|}{ Coeff } & multicolumn{1}{c|}{ Std Error } & T Stat & P-value \ hline Intercept & -5.5146 & 7.2273 & -0.7630 & 0.4493 \ hline Income & 0.4262 & 0.0392 & 10.8668 & 0.0000 \ hline Family Size & 5.5437 & 1.6949 & 3.2708 & 0.0020 \ hline end{tabular} What is the predicted house size (in hundreds of square feet) for an individual with a family size of 2 and an income of ( $ 100,000 ) ?
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The income is given in thousands of dollars, so $100,000 becomes 100. The regression equation is given by: Size of house = Intercept + (Income Coefficient * Income) + (Family Size Coefficient * Family Size) Substituting the given values into the equation: Show more…
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A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below: Regression Statistics Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50 ANOVA df SS MS F Significance F Regression 37043.3236 18521.6618 0.0000 Residual 14487.7627 308.2503 Total 49 51531.0863 Coefficients Standard Error t Stat P-value Intercept -5.5146 7.2273 -0.7630 0.4493 Income 0.4262 0.0392 10.8668 0.0000 Size 5.5437 1.6949 3.2708 0.0020 Also SSR( X 1 | X 2 ) = 36400.6326 and SSR( X 2 | X 1 ) = 3297.7917 Referring to Scenario 13-4, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000 and having a family size of 4?
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A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA df SS MS F Signif F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000 Coeff StdError t Stat p-value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 Referring to Table 14-4, which of the independent variables in the model are significant at the 5% level? Income, School Income, Size Size, School Income, Size, School
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