Answered Essay: The following data give the selling price, square footage, number of bedrooms, and age of

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 regression models to predict the selling price based upon each of the other factors individually. Which of these is best?

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Selling Price($) Square Footage Bedrooms Age (Years)
84,000 1,670 2 30
79,000 1,339 2 25
91,500 1,712 3 30
120,000 1,840 3 40
127,500 2,300 3 18
132,500 2,234 3 30
145,000 2,311 3 19
164,000 2,377 3 7
155,000 2,736 4 10
168,000 2,500 3 1
172,500 2,500 4 3
174,000 2,479 3 3
175,000 2,400 3 1
177,500 3,124 4 0
184,000 2,500 3 2
195,500 4,062 4 10
195,000 2,854 3 3

Expert Answer

So, using the Correlation r and Linear regression the models are defined:

So,

n= 17
X Y X^2 XY
Count Square Footage Selling Price($)
1 1,670 84,000 2788900 140280000
2 1,339 79,000 1792921 105781000
3 1,712 91,500 2930944 156648000
4 1,840 1,20,000 3385600 220800000
5 2,300 1,27,500 5290000 293250000
6 2,234 1,32,500 4990756 296005000
7 2,311 1,45,000 5340721 335095000
8 2,377 1,64,000 5650129 389828000
9 2,736 1,55,000 7485696 424080000
10 2,500 1,68,000 6250000 420000000
11 2,500 1,72,500 6250000 431250000
12 2,479 1,74,000 6145441 431346000
13 2,400 1,75,000 5760000 420000000
14 3,124 1,77,500 9759376 554510000
15 2,500 1,84,000 6250000 460000000
16 4,062 1,95,500 16499844 794121000
17 2,854 1,95,000 8145316 556530000
Sum 40,938 25,40,000 104715644 6429524000
a = 26532.23614
b = 51.02721153
Y = a+ bX
r= 0.83664028

Similarly for Bedrooms:

n= 17
X Y X^2 XY
Count Bedrooms Selling Price($)
1 2 84,000 4 168000
2 2 79,000 4 158000
3 3 91,500 9 274500
4 3 1,20,000 9 360000
5 3 1,27,500 9 382500
6 3 1,32,500 9 397500
7 3 1,45,000 9 435000
8 3 1,64,000 9 492000
9 4 1,55,000 16 620000
10 3 1,68,000 9 504000
11 4 1,72,500 16 690000
12 3 1,74,000 9 522000
13 3 1,75,000 9 525000
14 4 1,77,500 16 710000
15 3 1,84,000 9 552000
16 4 1,95,500 16 782000
17 3 1,95,000 9 585000
Sum 53 25,40,000 171 8157500
a = 20331.63
b = 41403.06
Y = a+ bX
r= 0.658192

ANd for Age

n= 17
X Y X^2 XY
Count Age (Years) Selling Price($)
1 30 84,000 900 2520000
2 25 79,000 625 1975000
3 30 91,500 900 2745000
4 40 1,20,000 1600 4800000
5 18 1,27,500 324 2295000
6 30 1,32,500 900 3975000
7 19 1,45,000 361 2755000
8 7 1,64,000 49 1148000
9 10 1,55,000 100 1550000
10 1 1,68,000 1 168000
11 3 1,72,500 9 517500
12 3 1,74,000 9 522000
13 1 1,75,000 1 175000
14 0 1,77,500 0 0
15 2 1,84,000 4 368000
16 10 1,95,500 100 1955000
17 3 1,95,000 9 585000
Sum 232 25,40,000 5892 28053500
a = 182504.7
b = -2424.91
Y = a+ bX
r= -0.83826

Hence of all the factors

Square Footage

Has a very high correlation of 0.836 and so is positively correlated and so that model should be used and is the best.

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