Question

Aregression analysis was conducted to investigate the factors that affect the sale price of oceanside condo units on the eastern coast of Florida. The following data were recorded for each of the 209 units sold. price = sale price in $1000s floor = floor height (floors 1 through 8 in the building) dist = distance from the elevator, measured on a scale from 1 to 15 view = 1 if the unit has an ocean view; 0 otherwise. furnish = 1 if the unit is furnished; otherwise. The Excel output for the following model (Model 1) was given below. Model 1: price = Bo + B1 floor + B2dist + B3 view + B4 furnish + B5 floor * dist +€ ANOVA df SS MS F 5 Regression Residual 119121.962 Total 208 238892.775 Coefficients Standard Error t Stat P-value Intercept 140.319 12.036 11.658 0.000 floor - 1.010 1.510 -0.669 0.504 dist 3.204 0.823 3.893 0.000 view 40.708 3.437 furnish 32.285 9.512 floor* dist -0.341 0.165

a. what percentage of the variation in sale price has been explained by the regression model?

b.Conduct an F test to determine overal significance, using alpha=0.05. Include test statistic value, p-value, critical value, conclusion.

c.Conduct a t test to determine whether the sale price of a condo unit with an ocean view is, on average, $32,000 higher than the sale price of a condo unit without an ocean view after accounting for the effects of the other independent variables. Use a 0.05 level of significance. Compute the test statistic value. and P-value with a conclusion.

Answer 1

a) R2 SS Regression 119770.8130 = 0.5014 SS Residual 238892.775 The 50.14 percentage of the variation in sale price has been explained by the regression model b) The null and alternative hypotheses are: Ho: B1=B2=B3=B4=Bs=0 Hj: At least one B's different from zero. Regression Residual Total df SS MS F 5119770.813 23954.1626 40.8211 203 119121.962 586.8077 208 238892.775 The test statistic value: F = 40.8211 P-value=0.0000 Critical value of F at (5, 203) df and 0.05 significance level= 2.2586 Conclusion: The value of test statistic is greater than critical value of F. Hence we reject null hypothesis and conclude that model is significant.

c) The null and alternative hypotheses are: Ho: B3= $32,000 Hi: B3> $32,000 40.708-32 The test statistic value: t = 3.437 2.5336 P-value =0.0060 Critical value oft at 203 df and 0.05 significance level= 1.65 Conclusion: The value of test statistic is greater than critical value of t. Hence we reject null hypothesis and conclude that the sale price of a condo unit with an ocean view is, on average, $32,000 higher than the sale price of a condo unit without an ocean view after accounting for the effects of the other independent variables.