Question

1. One Price Realty Company wants to develop a model to estimate the value of houses in its inventory The office manager has decided to develop a multiple regression model to help explain the variation in house values. (25 points) The office manager has chosen the following variables to develop the model: X1 square feet X2- age in years x3- dummy variable for house style (1 if ranch, 0 if not) X4-2d dummy variable for house style (I if split level, O if not) Y- house value Data on 15 houses were selected and an analysis conducted. A regression analysis of the One Price Realty houses was conducted with the results shown below. Fill in the ANOVA table as needed to help answer the following questions. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 4,038.25 15 MS Regression Residual Total 386,567,555 1709 344 521 Coefficients Standard Error Stot 116,026.73 22.50 735.51 991.17 1,589.86 8,550.31 4.57 259.66 2,454.96 3,561.02 Intercept Sq. Ft. Age (Years) Split Level Using the estimated regression model, what house value does the model predict when Sq. Ft. is 2,200, the Age is 11 years, and the house style is a Ranch? a. b. At the alpha- 0.01 level of significance, does the overall model explain a significant amount of the variation in the dependent variable, House Value? Suppose a house does not differ on any of the independent variables, except style. What is the average difference of House Value between a ranch style and a split level style? c. Using a confidence interval, is the population slope coefficient for Age significant at the 95% confidence? Perform the appropriate test to determine this. d

Answer 1

a) The regression equation is:

House Value = 116026.73 + 22.50 (Sq ft) - 735.51(Age) + 991.17(Ranch) + 1589.86(Split)

When Sq ft = 2200, Age = 11, Ranch = 1, Split = 0:

House Value = 116026.73 + 22.50 (2200) - 735.51(11) + 991.17(1) + 1589.86(0)
House Value = 158427.29

b) MS (Regression) = SS/df
df = number of predictors = 4
Hence, SS = MS*df = 4*386567555 = 1546270220

R-square tells us the significant amount of variation in the dependent variable = SS(Regression)/SS(Total)

R-square = 1546270220/1709344521 = 0.9045

Hence, variation explained is 90.45%

c) Coefficient of Ranch level = 991.17
Coefficient of Split Level = 1589.86

The average difference in the house value between the Ranch and Split level = 1589.86 - 991.17 = 598.69 (Split level being more of value)

D) To calculate the confidence interval, we will use the following formula:

b1 = -735.51

t (at 0.05 and df = n - k - 1 = 15 - 4 - 1 = 10): 2.228

S = Standard Error = 259.66

Lower bound: -735.51 - 2.228*259.66 = -1314.033

Upper bound: -735.51 + 2.228*259.66 = -156.988

Hence, as the confidence interval does not contain '0', we can conclude that the slope of age is significant in predicting the house value.