The equation below is designed to determine the effects of a home’s square foota

Question

The equation below is designed to determine the effects of a home’s square footage (sqrft), the number of bedrooms (bdrms), lot size (lotsize) and whether the house is a colonial-style house (colonial) on its price. Open the data set “Practice Exercise 3” in Excel. The data that you’ll need for this set of questions is in the sheet called “hprice1.” The codebook for “hprice1” is in the sheet called “hprice1 codebook.” Estimate the equation below via the multivariate regression approach.

Use the estimates to fill in the table below.

Standard Errors

Intercept

Bedrooms

Lot Size

Square Footage

Colonial

N

R2

*-Statistically-significant at the 95 percent confidence level

**-Statistically-significant at the 99 percent confidence level

***-Statistically-significant at the 99.9 percent confidence level

Please answer the following questions:

1.Is the effect of square footage on a house’s price statistically significant?

2.Is the effect of the number of bedrooms on a house’s price statistically-significant?

3.There are two houses that are identical, except that the square footage of one is 600 square feet larger than the other. What is the predicted difference in their prices?

4.What is the estimated increase in price for a house with an additional bedroom that is 140 square feet in size?

5.Interpret the coefficient on lotsize. Is it statistically significant?

6.The first house in the sample has sqrft = 2,439, bdrms = 4, lotsize=6,126,colonial=1. Find the predicted selling price for this house from the estimated equation.

7.The actual selling price of the first house in the sample was $300,000. Compare this to your answer in (vii). Does the comparison suggest that the buyer overpaid or underpaid for the house?

8.What has to be true about your analysis in order for the comparison that you made in part (viii) to be valid?

Standard Errors

Intercept

Bedrooms

Lot Size

Square Footage

Colonial

N

R2

Explanation / Answer

The multiple regression model is

Price =b0+b1 bdrms+b2 lotsize+b3 sqrft+b4 colonial

1. There is a positive and statistically significant effect between square footage and house’s price

2. There is not statistically significant effect between the number of bedrooms and house’s price because the p-value is grater than 0.05

3. If one have x sqrft, the other is x+600 sqrt

predicted difference in their prices is 124.2375*600=74542.49

4.The estimated increase in price for a house with an additional bedroom that is 140 square feet in size is

11004.29+124.2375*140=28397.54

6. The estimated equation is

Price =-24126.5+11004.29bdrms+2.075 lotsize+124.23sqrft+13715.54colonial

The first house in the sample has sqrft = 2,439, bdrms = 4, lotsize=6,126,colonial=1.

The predict price is

price=$349337.9

7. The actual selling price of the first house in the sample was $300,000. The comparison suggest that the buyer overpaid for the house.

SUMMARY OUTPUT Regression Statistics Multiple R 0.822066 R Square 0.675792 Adjusted R Square 0.660167 Standard Error 59876.97 Observations 88 ANOVA df SS MS F Significance F Regression 4 6.2E+11 1.55E+11 43.2521 1.45E-19 Residual 83 2.98E+11 3.59E+09 Total 87 9.18E+11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -24126.5 29603.45 -0.81499 0.41741 -83006.6 34753.55 bdrms 11004.29 9515.26 1.156489 0.250799 -7921.18 29929.76 lotsize 2.075832 0.642651 3.230108 0.001774 0.797625 3.35404 sqrft 124.2375 13.33826 9.31437 1.53E-14 97.70822 150.7667 colonial 13715.54 14637.27 0.937029 0.351462 -15397.4 42828.47

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