Question

4. The realtors from problem #2 wants to explore how location and size impacts the selling price for single-family houses. The realtors plans to use number of rooms as an indicator of size. Location will be whether the home is located on the east side of town (=0) or west side of town (=1). The data she collected from 20 homes is located in the data file Homes.

a. Run a multiple regression using number of rooms and neighborhood location to predict selling price. Report your regression equation.

b. Is the regression model you ran statistically significant? How can you tell?

c. What is the relationship (correlation) between the predictors and selling price?

d. How much variance in selling price is explained by the predictors?

e. Which of your predictors explain a unique amount of variance in selling price?

f. Predict the selling price of a home on the east side of town with 8 rooms. Predict the selling price of a home on the west side of town with 8 rooms. Explain the difference between the two selling price estimates.

Price	Rooms	Neighborhood
$          309,600	7	0
$          307,400	8	0
$          340,300	9	0
$          346,500	12	0
$          298,200	6	0
$          337,800	9	0
$          324,100	10	0
$          313,200	8	0
$          327,800	9	0
$          325,300	8	0
$          308,500	6	1
$          381,300	13	1
$          337,400	10	1
$          346,200	10	1
$          342,400	9	1
$          323,700	8	1
$          329,600	8	1
$          343,600	9	1
$          360,700	11	1
$          348,300	9	1

Answer 1

a. Run a multiple regression using number of rooms and neighborhood location to predict selling price. Report your regression equation.

Y = 2,43,737.1327 + 9,218.9381*X1 + 12,696.7434*X2

b. Is the regression model you ran statistically significant? How can you tell?

The hypothesis being tested is:

H₀: β₁ = β₂ = 0

H₁: At least one β_i ≠ 0

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

c. What is the relationship (correlation) between the predictors and selling price?

r = 0.931

d. How much variance in selling price is explained by the predictors?

R² = 0.867

e. Which of your predictors explain a unique amount of variance in selling price?

Both X1 and X2

f. Predict the selling price of a home on the east side of town with 8 rooms. Predict the selling price of a home on the west side of town with 8 rooms. Explain the difference between the two selling price estimates.

Y = 2,43,737.1327 + 9,218.9381*8 + 12,696.7434*1 = 330185.3805