A realtor used the regression model y beta0 beta1x1 beta2x

A realtor used the regression model, y = beta0 + beta1x1 +beta2x2 + epsilon, to predict selling prices of homes (in thousands of $) in a region of California. The variable x1 represents the home size (square feet), and x2 represents the number of bedrooms.

ANOVA

Source             DF            SS                  MS            F

Regression        2         6101.6

Error                              219.6

Total                 10

                         Coefficient         Standard Error        t statistic

  Intercept          26.28                        22.88                1.15

       Size          0.12352                    0.02435              5.07

Bedrooms         20.183                        6.697                3.01

How many homes are included in the sample?          

10

11

28

13

Solution

The degrees of freedom is:

N-k-1=10 , where k= number of variables

N-3-1=10

N=10+4=14

But, if one has N data points then she can fit the points exactly with a polynomial of degree N-1.

Thus, the number of homes are included in the sample is 14-1=13