Question

Question 1

Suppose we wanted to predict the selling price of a house using its size in a certain area of a city. A random sample of six houses were selected from the area. The data is presented in the following table with size given in hundreds of square feet, and sale price in thousands of dollars.

Size (Xi)	12	15	18	21	24	27
Price (Yi)	60	85	75	105	120	110

a)         Find the least squares estimate for the regression line Y_i= b₀+ b₁X_i+ e_i.

b) What would be your estimate of the sale price for a 2,000 square foot house?

c)  Estimate the standard deviation of the error term e_i

d)  Compute the correlation coefficient.

e)   What proportion of the variability in the sale price can be explained using this model   (i.e. what is R²)?

f)    Test the null hypothesis that b₁= 0 (perform a two-sided test), using α = 0.05. Is the model useful?

g)   Perform the regression using SAS, and give the p-value to the test in part f ). Verify that the p-value agrees with your conclusion in part f ).

Answer 1