The following data give the selling price, square footage, number of bedrooms, a
ID: 3135479 • Letter: T
Question
The following data give the selling price, square footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months. Develop three simple linear regression models to predict the selling price based upon each of the other factors individually. Which of these is better?
SELLINMG PRICES($)
SQUARE FOOTAGE
BEDROOMS
AGE (YEARS)
263,000
1,545
2
20
267,500
1,812
3
28
279,000
1,940
3
36
287,500
2,400
3
16
292,500
2,334
3
26
295,000
2,411
3
21
353,000
2,477
3
9
355,000
2,936
4
8
388,000
2,640
3
1
392,500
2,670
4
2
394,000
2,679
3
3
395,000
2,510
3
1
404,000
2,800
4
2
565,500
3,262
5
8
431,000
2,854
4
2
Use the data in problem #4 and develop a multiple regression model to predict selling price based on the square footage, number of bedroom, and age. Please write down the multiple regression equation. Use this to predict the selling price of a 6-year-old, 3,000-square-foot house with 4 bedrooms.
SELLINMG PRICES($)
SQUARE FOOTAGE
BEDROOMS
AGE (YEARS)
263,000
1,545
2
20
267,500
1,812
3
28
279,000
1,940
3
36
287,500
2,400
3
16
292,500
2,334
3
26
295,000
2,411
3
21
353,000
2,477
3
9
355,000
2,936
4
8
388,000
2,640
3
1
392,500
2,670
4
2
394,000
2,679
3
3
395,000
2,510
3
1
404,000
2,800
4
2
565,500
3,262
5
8
431,000
2,854
4
2
Explanation / Answer
Sol)
The Regression model is
y= a+bX1+cX2+dX3
From Excel
The fitted regression equation is
y=130192.5 +26.69 X1 +58028.04X2 - 2665.06 X3
Now predict the selling price of a 6-year-old, 3,000-square-foot house with 4 bedrooms.
y=130192.5 +26.69 X1 +58028.04X2 - 2665.06 X3
y=130192.5 +26.69 (3000) +58028.04(4) - 2665.06 (6)
y= 4,26,384
SUMMARY OUTPUT Regression Statistics Multiple R 0.901234 R Square 0.812224 Adjusted R Square 0.761012 Standard Error 39623.53 Observations 15 ANOVA df SS MS F Significance F Regression 3 7.47E+10 2.49E+10 15.8601 0.000262 Residual 11 1.73E+10 1.57E+09 Total 14 9.2E+10 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 130192.5 104743.8 1.242961 0.239724 -100347 360732 SQUARE FOOTAGE 26.69224 62.89177 0.424416 0.679445 -111.732 165.1161 BEDROOMS 58028.04 30122.1 1.926427 0.080272 -8270.26 124326.3 AGE (YEARS) -2659.06 1474.083 -1.80388 0.098675 -5903.5 585.3691Related Questions
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