The following data gives the selling price, square footage, number of bedrooms,
ID: 3023509 • Letter: T
Question
The following data gives 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? (Please provide entire formula's for every step)
Selling Price ($) Square Footage Bedrooms Age (Years) 84000 1670 2 30 79000 1339 2 25 91500 1712 3 30 120000 1840 3 40 127500 2300 3 18 132500 2234 3 30 145000 2311 3 19 164000 2377 3 7 155000 2736 4 10 168000 2500 3 1 172500 2500 4 3 174000 2479 3 3 175000 2400 3 1 177500 3124 4 0 184000 2500 3 2 195500 4062 4 10 195000 2854 3 3Explanation / Answer
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
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 20326991.77Related Questions
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