In a study of housing demand, a county assessor is interested in developing a regression model to estimate the selling price of residential

Question

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

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Ngọc Diệp 1 month 2021-08-12T07:50:31+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-08-12T07:52:26+00:00

    Answer:

    y = 78.4286×1 + 7170.2361×2 – 236.2895×3 – 5663.3894×4 – 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 = 78.4286×1 + 7170.2361×2 – 236.2895×3 – 5663.3894×4 – 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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