Seattle home Prices. Home prices are often modeled by looking at the square foot

Question

Seattle home Prices. Home prices are often modeled by looking at the square footage of a home, number of bathrooms and other characteristics. One interesting question is if even after taking into account these characteristics is there evidence for differences in the listing prices for different Realtors? Is it realistic to assume that some Realtors tend to under or over valuate their listed properties? This dataset has information on the sales prices of 36 homes listed in the Seattle area. Of these homes, 28 were listed by one Realtor while 8 of the homes were listed by a different Realtor. In this dataset we also have information on the price of the listings in thousands of dollars, the total square feet, the price in dollars per square feet, the Realtor indicator, the number of bedrooms and the number of bathrooms. • Response Variable — Price ($000) — The dollar sales of the convenience store • Explanatory Variables • Square Feet — The total number of square feet in the home • Price/Sq Ft — The listing price (in dollars) per square foot • Realtor — A categorical variable indicating the Realtor • Bedrooms — Number of bedrooms • Bathrooms — Number of bathrooms

2

1. Create a model using all quantitative variables to predict price.

2. Based on the EDA we performed, do you have any concerns regarding the model we built in the previous part? Why or why not?

3. Is your overall model useful? Provide the results of a hypothesis test.

4. Which individual variables are useful for predicting price based on individual t-tests? Is this what you expected based on the EDA you performed?

5. Consider adding the categorical variable (and remove price/sq. foot, as well as any other variables you believe should be removed based on the previous questions). How many coefficients will be added to your model to incorporate Realtor?

6. Interpret the coefficient for realtor for the model you built in part 5.

7. Interpret the coefficient for square footage for the model you built in part 5.

8. Interpret the R-squared for this model.

9. Predict the price for a home sold by Realtor A, with 3 bedrooms and 2 bathrooms, and 1500 square feet. Do you think the prediction is close to what you would expect in reality? Explain.

10. Based on the plots in questions 1 and 2 of the EDA portion, do you think we should consider adding additional terms to this model? What is the benefit of not adding additional terms to your model?

Price Square Feet Price/SqFt Realtor Bedrooms Bathrooms 225 868 0.25921659 A 1 1 212 1021 0.20763957 A 3 2 210 1164 0.18041237 A 3 1 330 1598 0.20650814 A 3 3 165 888 0.18581081 A 2 1 300 1210 0.24793388 A 3 2 320 1295 0.24710425 A 2 2 210 1360 0.15441176 A 3 2 255 1440 0.17708333 A 3 2 229 1567 0.14613912 A 3 2 296 1767 0.16751556 A 3 2 450 1796 0.25055679 A 3 2 448 1940 0.23092784 A 2 1 285 1963 0.14518594 A 4 3 418 2022 0.20672601 A 4 2 319 2038 0.15652601 A 4 3 345 2690 0.12825279 A 4 3 272 2126 0.12793979 A 4 3 342 2163 0.15811373 A 3 3 455 2190 0.20776256 A 3 3 580 2320 0.25 A 3 2 496 2420 0.20495868 A 4 3 575 2452 0.23450245 A 3 2 625 2690 0.23234201 A 4 2 495 2930 0.16894198 A 4 3 524 3260 0.1607362 A 4 3 355 3049 0.11643162 A 3 3 255 1620 0.15740741 A 3 3 600 2167 0.27688048 B 3 2 599 1350 0.4437037 B 2 1 590 1630 0.36196319 B 3 2 580 1645 0.35258359 B 3 2 580 2300 0.25217391 B 4 2 575 2773 0.20735665 B 4 2 550 2490 0.22088353 B 3 1 600 1635 0.36697248 B 2

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Explanation / Answer

1)

2)

In this model, we are using square feet and price per square feet to predict the price which shouldnt ideally be the case and we should ideally use square feet to predict

3)

Model is overall significant because F>Significance F. We can conclude that one of the independent variables is predicting the dependent variable.

4)

Looking at the t-test and p-values (all p-values are less than 0.05 and hence they are significant), we can say that almost all of the variables are significant.

SUMMARY OUTPUT Regression Statistics Multiple R 0.980007795 R Square 0.960415278 Adjusted R Square 0.955307572 Standard Error 31.32559462 Observations 36 ANOVA df SS MS F Significance F Regression 4 738060.2263 184515.0566 188.0326054 0.00 Residual 31 30420.07922 981.2928782 Total 35 768480.3056 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -347.9102312 38.80813587 -8.964878715 0.00 -427.0599461 -268.7605163 Square Feet 0.184354746 0.011585769 15.91217239 0.00 0.160725415 0.207984076 Price/SqFt 1696.372584 85.25336798 19.89801252 0.00 1522.497193 1870.247974 Bedrooms 25.15234648 10.72116012 2.346047087 0.03 3.286396247 47.01829671 Bathrooms -22.21939059 10.35954649 -2.144822712 0.04 -43.34782495 -1.090956229

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