2

2. Consider the model 
+Pz, +P3.3+, 
suppose that application of least squares to 20 observations on these variables yields the following results 
[J [?..37] ++(b)[O.O2:gi .77 —0.05 —0.03 0 
Test the hypothesis Hai.32 IIint: this is the same 
 

3. The following regression was run in R 
In (price) = (31 + 32age + 133age2 + [34sqft + f36(beds * sqft) + e 
Coefficients: 
Estimate Std. Error t value Pr(>ItI) (Intercept) 4.146e+00 3.494e-02 118.670 < 2e-16 *** age -1.892e-02 1.432e-03 -13.213 < 2e-16 *** I(ageA2) 2.086e-04 2.427e-05 8.592 < 2e-16 *** sqft 4.823e-02 3.019e-03 15.976 < 2e-16 *** I(bedrooms * sqft) -1.825e-03 6.047e-04 -3.018 0.00262 ** 
a. Find and interpret the marginal effect of age for a 10 yr old house. 
b. Find and interpret the marginal effect of sqft for a 3 bedroom house. 
c. How does the marginal effect of sqft change for every additional room in the house?