In: Statistics and Probability
Use the data below to solve. The data gives the square footage and sales prices for several houses in Bellevue, Washington. Use this information to solve the following:
PLEASE SHOW YOUR WORK : )
1) You plan to build a 500 square foot addition to your home. How much do you think your home value will increase as a result?
2) What percentage of the variation in home value is explained by the variation in the house size?
3) A 3000 square foot home is listed for $500,000. Is this price out of line with typical sales in Bellevue? What might cause this discrepancy?
Square Footage Value
2000 238139.3695
2200 259711.9508
2400 300953.668
3000 369965.7313
3200 340091.2955
3600 405425.021
2900 345131.0331
Independent variable (X): Square Footage
Dependent variable (Y): Value
First we need to find the regression equation. Following table shows the calculations:
X | Y | X^2 | Y^2 | XY | |
2000 | 238139.3695 | 4000000 | 56710359306 | 476278739 | |
2200 | 259711.9508 | 4840000 | 67450297388 | 571366292 | |
2400 | 300953.668 | 5760000 | 90573110283 | 722288803 | |
3000 | 369965.7313 | 9000000 | 1.36875E+11 | 1109897194 | |
3200 | 340091.2955 | 10240000 | 1.15662E+11 | 1088292146 | |
3600 | 405425.021 | 12960000 | 1.64369E+11 | 1459530076 | |
2900 | 345131.0331 | 8410000 | 1.19115E+11 | 1000879996 | |
Total | 19300 | 2259418.069 | 55210000 | 7.50755E+11 | 6428533245 |
That is for each addition square footage value is increased by $99.6398. So for additional 500 square footage, value is increased by
500 * 99.6398 = 49819.9
Answer: $49819.90
(b)
That is 92.4% of the variation in home value is explained by the variation in the house size.
(c)
According to regression line, the value of house with 3000 square foot is $346972.247. So price $500,000 is out of line with typical sales in Bellevue. It may be due to location of house or amenities of house (like parking space etc).