Question

1. You are conducting a study on the real estate market in Los Angeles county. According to the data you collected, you generated a sample regression line of

yˆ = 347 + .257x1 − .192x2 + 241x3

y is the price of a home in thousands of dollars

x1 is the size of the home in square feet

x2 is the age of the home in years

x3 is a dummy variable that is equal to 1 if the house is in Beverly Hills city limits, 0 otherwise.

(a) Interpret the coefficient of x1.

(b) Interpret the coefficient of the dummy variable, x3.

(c) The p-value of the t-test statistic for the test H0 : β3 = 0 against H1 : β3 6= 0 is equal to .20182. Would you reject or fail to reject the null hypothesis at the α = .05 significance level? Does this line up with your perception of the price of a home in Beverly Hills vs. other parts of Los Angeles county?

(d) The 95% confidence interval for β2 is (−.2, .08). Would you reject or fail to reject the null hypothesis for the test H0 : β2 = 0 against H1 : β2 6= 0 at the α = .05 significance level? Why?

Answer 1

(a) there is increase in price by 0.267 unit with unit change in x1 keeping other things/variable constant,

(b) there is increase in price by 241 unit with unit change in x3 keeping other things/variable constant,

that is if home in Beverly Hills , its price will be more by 241 units if other things remain unchanged

(c) since p-value=0.20182. is more than alpha=0.05, so we fail to reject H0(or accept H0)

(d) since 0 lies in the interval (−.2, .08)., so we fail to reject H0(or accept H0)