Use the data in Problem 4-22 and develop a regression model to predict selling p

ID: 3024364 • Letter: U

Question

Use the data in Problem 4-22 and develop a regression model to predict selling price based on the square footage, number of bedrooms, and age. Ust this to predict the selling price of a 10-year-old, 2,000-square-foot house with three bedrooms. (Reminder: ALL FORMULAS AND EQUATIONS USED TO GENERATE ANSWERS NEED TO BE SHOWN TO RECEIVE FULL CREDIT FOR THE PROBLEM).

Here is the information from 4-22:

Line of Regression Y on X i.e Y = bo + b1 X

1st Model: B/W Square Footage, Selling Price

Mean of X = X / n =    2408.1176
Mean of Y = Y / n =   149411.7647
(Xi - Mean)^2 =   6132123.76
(Yi - Mean)^2 =   22810617647
(Xi-Mean)*(Yi-Mean) =   312905176.5
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 312905176.46 / 6132123.76 = 51.0272
bo = Y / n - b1 * X / n
bo = 149411.7647 - 51.0272*2408.1176 = 26532.2384

Y = bo + b1 X

Y'=26532.2384+51.0272*X

2nd Model: B/W Bedrooms, Selling Price

Mean of X = X / n =    3.1176
Mean of Y = Y / n =   149411.7647
(Xi - Mean)^2 =   5.77
(Yi - Mean)^2 =   22810617647
(Xi-Mean)*(Yi-Mean) =   238676.44
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = 238676.44 / 5.77 = 41365.0676
bo = Y / n - b1 * X / n
bo = 149411.7647 - 41365.0676*3.1176 = 20452.03

Y = bo + b1 X

Y'=20452.03+41365.0676*X

3rd Model: B/W Bedrooms, AGE

Mean of X = X / n =    13.6471
Mean of Y = Y / n =   149411.7647
(Xi - Mean)^2 =   2725.88
(Yi - Mean)^2 =   22810617647
(Xi-Mean)*(Yi-Mean) =   -6610029.42
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = -6610029.42 / 2725.88 = -2424.9158
bo = Y / n - b1 * X / n
bo = 149411.7647 - -2424.9158*13.6471 = 182504.8328

Y = bo + b1 X

Y'=182504.8328-2424.9158*X

The Three Model Regression Eqn are

i. Y'=26532.2384+51.0272*X

ii. Y'=20452.03+41365.0676*X

iii. Y'=182504.8328-2424.9158*X

2nd Model be the Best Fit, as we get the better selling price for every increment of x

Here is the information from 4-22:

Line of Regression Y on X i.e Y = bo + b1 X

1st Model: B/W Square Footage, Selling Price

Sqr Foot Selling Pr (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 1670 84000 544817.591 4.279E+09 48281574.77 1339 79000 1143012.443 4.958E+09 75278456.89 1712 91500 484579.713 3.354E+09 40313398.65 1840 120000 322757.607 865051903 16709341.17 2300 127500 11689.415 480125432 2369047.41 2234 132500 30316.939 286007785 2944635.88 2311 145000 9431.828 19463668 428460 2377 164000 968.305 212816609 -453950.87 2736 155000 107506.868 31228374 1832284 2500 168000 8442.375 345522492 1707931.67 2500 172500 8442.375 533066609 2121402.47 2479 174000 5024.315 604581315 1742873.13 2400 175000 65.895 654757786 -207715.06 3124 177500 512487.611 788948962 20107873.3 2500 184000 8442.375 1.196E+09 3178050.07 4062 195500 2735326.993 2.124E+09 76224521.21 2854 195000 198811.115 2.078E+09 20326991.77

2nd Model: B/W Bedrooms, Selling Price

BED ROOM Selling Pr (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 2 84000 1.249 4.279E+09 73104.19 2 79000 1.249 4.958E+09 78692.19 3 91500 0.014 3.354E+09 6810.42 3 120000 0.014 865051903 3458.82 3 127500 0.014 480125432 2576.82 3 132500 0.014 286007785 1988.82 3 145000 0.014 19463668 518.82 3 164000 0.014 212816609 -1715.58 4 155000 0.779 31228374 4931.06 3 168000 0.014 345522492 -2185.98 4 172500 0.779 533066609 20373.06 3 174000 0.014 604581315 -2891.58 3 175000 0.014 654757786 -3009.18 4 177500 0.779 788948962 24785.06 3 184000 0.014 1.196E+09 -4067.58 4 195500 0.779 2.124E+09 40668.26 3 195000 0.014 2.078E+09 -5361.18

3rd Model: B/W Bedrooms, AGE

AGE Selling Pr (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 30 84000 267.417 4.279E+09 -1069672.05 25 79000 128.888 4.958E+09 -799377.72 30 91500 267.417 3.354E+09 -947025.3 40 120000 694.475 865051903 -775085.29 18 127500 18.948 480125432 -95379.72 30 132500 267.417 286007785 -276556.4 19 145000 28.654 19463668 -23615.74 7 164000 44.184 212816609 -96969.46 10 155000 13.301 31228374 -20380.85 1 168000 159.949 345522492 -235087.27 3 172500 113.361 533066609 -245822.75 3 174000 113.361 604581315 -261793.4 1 175000 159.949 654757786 -323616.97 0 177500 186.243 788948962 -383322.96 2 184000 135.655 1.196E+09 -402852.64 10 195500 13.301 2.124E+09 -168088.4 3 195000 113.361 2.078E+09 -485382.5

The Three Model Regression Eqn are

i. Y'=26532.2384+51.0272*X

ii. Y'=20452.03+41365.0676*X

iii. Y'=182504.8328-2424.9158*X

2nd Model be the Best Fit, as we get the better selling price for every increment of x

Explanation / Answer

Answer :

i) Y' = 26532.2384 + 51.0272* ( 2000) = 128586.6354

ii) Y' = 20452.03 + 41365.0676 * (2000) = 82750587.23

iii) Y' = 182504.8328 - 2424.9158 * (2000) = - 4667326.767

model 2 is the best fit

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