Results for a multivariate regression model predicting monthly rent based on several variables are shown above. For your convenience, here are definitions for each variable.

Y = Rent = monthly rent payment measured in dollars

X1 = Family_Size: the number of people living in the apartment

X2 = Income = family income measured in dollars

X3 = Southwest = a dummy variable equal to one if the apartment is in the Southwest region of the United States

X4 = Northwest = a dummy variable equal to one if the apartment is in the Northwest region

X5 = Northeast = a dummy variable equal to one if the apartment is in the Northeast region

***The base category is living in the Southeast region" ***

(Questions)

(a) Using the test statistic method, do a hypothesis test for whether there is a statistically significant relationship between family size and monthly rent. Show all steps to your hypothesis test and use a significance level of 5%. (5 points)

(b) Type the value of the y-intercept and explain the meaning of that number. (4 points)

(c) Is the following statement TRUE or FALSE? Explain your answer. (5 points)

"This regression model fails to control for the effect of living in the Southeast region of the US when estimating monthly rates of rent. "