The equation below is designed to determine the effects of a

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

Solution

Following is the output obtained from the excel after running the multiple regression at 95% confidence level on the given data set -

So, the required regression equation is -

Price = -40447.665+904.078(assets)+9630.256(bdrms)+0.5993(lotsize)+1.0713(sqrft)+9547.571(colonial)

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1)

As the p-value of the square footage (i.e. 0.950475) significantly larger than the significance level of 0.05, 0.01 and 0.001, so we can say that the effect of square footage on house price is statistically significant at all the three confidence levels.

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2)

As the p-value of the number of bedrooms (i.e 0.16756) larger than the significance level of 0.05, 0.01 and 0.001, so we can say that the effect of number of bedrooms on house price is statistically significant at all the three confidence levels.

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3)

The coefficient of the variable determines the change in price of the house due to an unit change in that variable. The coefficient of square footage is +1.071364, that means if we increase the square footage by 1 unit then the price will increase by $1071.364 (as the prices are in $1000).

So, for the difference of 600 square foots, the difference in price is = 600 x $1071.364 = $642818.4

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4)

The coefficient of square footage is +1.071364, that means if we increase the square footage by 1 unit then the price will increase by $1071.364.

And the coefficient of number of bedrooms is +9630.256, that means if we increase the square footage by 1 unit then the price will increase by $9630256 (as the prices are in $1000).

Now, the two variables are changing here. Both the number of bedrooms (bdrms) and the square footage (sqrft) are changing. The variable bdrms is increasing by 1 unit and the variable sqrft is increasing by 140 units. So, the price increase = $9630256 +(140) $1071.364 = $9630256 + $149990.96 = $9780247

Hence, the increase in price will be $9780247.

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5)

The coefficient of variable lot size is 0.599268, that means a unit increase in the lot size will result in an increase of $599.268 to the price. The p-value of the coefficient is 0.23455, which is greater than the significance level 0.05, 0.01 and 0.001. So, the variable lot size is significant at all the three confidence levels.

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6)

The predicted value of the selling price for the first sample is -

P = -40447.665+904.078(349.1)+9630.256(4)+0.5993(6126)+1.0713(2439)+9547.571(1)

P = -40447.665+315613.63+38521.024+3671.3118+2612.9007+9547.571 = 329518.77

Hence, the predicted price of the house from first sample = 1000 x $329518.77 = $329518770

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7)

As the predicted price of the house is larger than the actual paid price, so we can say that the buyer underpaid for the house.

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8) In order to make our previous comparison significant, we need to ensure that the coefficient of determination of the model (i.e. r-square) is large. If the r-square value is large, it means that the predicted value is significant.

As the r-square value of our model is 0.8308, so we can say that it is a good predictive model. Hence our comparison is significant.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.91151731
R Square	0.8308638
Adjusted R Square	0.82055062
Standard Error	43510.9212
Observations	88
ANOVA
	df	SS	MS	F	Significance F
Regression	5	7.62612E+11	1.53E+11	80.56328	3.59114E-30
Residual	82	1.55242E+11	1.89E+09
Total	87	9.17855E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-40447.665	21594.19958	-1.87308	0.064621	-83405.40687	2510.077	-83405.407	2510.07702
assets	904.077925	104.2679069	8.670721	3.25E-13	696.6558425	1111.5	696.655843	1111.50001
bdrms	9630.25587	6916.289656	1.392402	0.167565	-4128.447486	23388.96	-4128.4475	23388.9592
lotsize	0.59926828	0.497077003	1.205584	0.231445	-0.389576227	1.588113	-0.3895762	1.58811279
sqrft	1.07136388	17.19658419	0.062301	0.950475	-33.13812017	35.28085	-33.13812	35.2808479
colonial	9547.57074	10647.34829	0.896709	0.372499	-11633.39681	30728.54	-11633.397	30728.5383