Question

In: Statistics and Probability

Use the data below to solve. The data gives the square footage and sales prices for...

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

Solutions

Expert Solution

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).

orchestra answered 2 years ago
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