A real estate builder wishes to determine how house size (House) is influenced b

Question

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 µltiple 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 901.4434 0.0001 Residual 1214.2264 26.9828 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 the tables, one individual in the sample had an annual income of $10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet) for this data point? a. 8.10 b. 5.40 c. -5.40 d. -8.10 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 µltiple 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 901.4434 0.0001 Residual 1214.2264 26.9828 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 the tables, one individual in the sample had an annual income of $10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet) for this data point? a. 8.10 b. 5.40 c. -5.40 d. -8.10 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 µltiple 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 901.4434 0.0001 Residual 1214.2264 26.9828 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 the tables, one individual in the sample had an annual income of $10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet) for this data point? a. 8.10 b. 5.40 c. -5.40 d. -8.10

Explanation / Answer

The following details of multiple regression analysis is referred from summary output

Intercept (a)

-1.6335

Income Coeff. (X1)

0.4485

Size Coeff. (X2)

4.2615

School Coeff. (X3)

-0.6517

The regression equation for house size is determined by following line:

Y = -1.6335 + (0.4485)(X1) + (4.2615)(X2) + (-0.6517)(X3)

Thus for the household, X1 = 10.000 (income in thousand), X2 = 1 (family size) and X3 = 8 (schooling)

Ycal (in thousands) = -1.6335 + (0.4485)(10) + (4.2615)(1) + (-0.6517)(8)

Ycal = 1.8994

Whereas, actual home owned by the individual is 10,000 square feet, (Ya = 10.00)

Residual = Actual – calculated = 10.00 – 1.8994 = 8.10

ANS: a. 8.10

Intercept (a)

-1.6335

Income Coeff. (X1)

0.4485

Size Coeff. (X2)

4.2615

School Coeff. (X3)

-0.6517

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