Question

 

29.5	1.5	7
27.9	1.175	6
25.9	1.232	6
29.9	1.121	6
29.9	0.988	6
30.9	1.24	7
28.9	1.501	6
35.9	1.225	6
31.5	1.552	6
31	0.975	5
30.9	1.121	6
30	1.02	5
36.9	1.664	8
41.9	1.488	7
40.5	1.376	6
43.9	1.5	7
37.5	1.256	6
37.9	1.69	6
44.5	1.82	8
37.9	1.652	6
38.9	1.777	8
36.9	1.504	7
45.8	1.831	8
25.9	0.998	7

A sample of 24 recently sold. The variables are: the sale price in $/10000 (Y), the size of the home in sq. ft./1000 (X₁), and the number of rooms (X₂).

Y	X1	X2
29.5	1.5	7
	…
25.9	0.998	7

a) Calculate SSR(X₂| X₁).

b) Calculate SSR(X₁²| X₁)

c) Test to see if the quadratic term is useful in the model

Y= B0 +B1X1 + B2X1^2 + E

d)   Calculate SSR(X₂, X₁X₂| X₁) and MSR(X₂, X₁X₂| X₁).

 

 

e)   Perform a nested models test to test H₀: B2=B3=0 in the model:

 

Y = B0 + B1X1 + B2X2 +B3X1X2 + E

 

 

f)    Which model would you use when trying to predict the sale price?

Answer 1

a) Regression Equation

y = 11.12 + 14.10 x1 + 0.61 x2

b) the value of SSE that is minimized by the least squares method=407.285

c) the estimate s, the standard deviation of the model=19.395

d) p-value for regression=0.001<0.05,we can say that the above model is a good one.

e) p-value for x1=0.005<0.05,so we can say x1 is important predictor to predict y

and p-value for x2=0.669,so we can say x2 does not have any significant effect to predict y

f) the coefficient of determination R2=50.87% and the adjusted coefficient of determinationRa2=39.50%

50.87% of variability of y has been explained by the multiple regression equation of x1 and x2.