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In a study of housing demand, a county assessor is interested in developing a regression model to estimate the selling price of residential properties within her jurisdiction. She randomly selects several houses and records the selling price in addition to the following values: the size of the house (in square feet), the total number of rooms in the house, the age of the house, and an indication of whether the house has an attached garage. These data are stored in the file HousingDemand.
A. Estimate and interpret a multiple regression equation that includes the four potential explanatory variables. How do you interpret the coefficient of the Attached Garage variable?
B. Evaluate the estimated regression equation’s goodness of fit.
C. Use the estimated equation to predict the sales price of a 3000-square-foot, 20-year-old home that has seven rooms but no attached garage. How accurate is your prediction?
House Selling Price Size # Rooms Age Attached Garage
1 $240,800 3070 7 23 1
2 $215,200 2660 6 23 1
3 $199,200 2390 7 20 1
4 $182,400 2240 6 9 0
5 $144,800 1500 7 17 0
6 $126,400 1440 7 8 0
7 $312,000 3720 9 31 1
8 $185,600 2520 7 15 1
9 $176,800 2160 7 8 0
10 $162,400 2140 8 20 1
11 $304,000 3000 8 15 1
12 $256,000 3000 8 18 1
13 $222,400 2700 7 17 1
14 $159,200 2020 7 18 0
15 $130,400 1200 6 17 0

Sagot :

Fichohidn

Answer:

y = 78.4286x1 + 7170.2361x2 - 236.2895x3 - 5663.3894x4 - 29470.2716

Goodness of fit = 0.8929

Predicted price = $251,281

Step-by-step explanation:

Selling price (Y) :

240800

215200

199200

182400

144800

126400

312000

185600

176800

162400

304000

256000

222400

159200

130400

Size (X1) :

3070

2660

2390

2240

1500

1440

3720

2520

2160

2140

3000

3000

2700

2020

1200

Room (x2) :

7

6

7

6

7

7

9

7

7

8

8

8

7

7

6

Age (X3) :

23

23

20

9

17

8

31

15

8

20

15

18

17

18

17

Attached garage (X4) :

1

1

1

0

0

0

1

1

0

1

1

1

1

0

0

Multiple regression model:

y = a1x1 + a2x2 + a3x3 + a4x4 + c

Where, a1, a2, a3, a4 are the Coefficients

c = intercept

The result of the multiple regression fit using a multiple regression calculator is :

y = 78.4286x1 + 7170.2361x2 - 236.2895x3 - 5663.3894x4 - 29470.2716

The cost of housing with an attached garage decreases by $5663.3894

Goodness of fit of the regression equation is 0.8929

Use the estimated equation to predict the sales price of a 3000-square-foot, 20-year-old home that has seven rooms but no attached garage.

Put values in the regression equation :

y = 78.4286(3000) + 7170.2361(7) - 236.2895(20) - 5663.3894(0) - 29470.2716

y = $251281.3911

Hence, predicted value is $251,281

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