Question

GBA 306 Statistical Methods of Business II – Case Study – Indiana Real Estate

Ann Perkins, a realtor in Brownsburg, Indiana, would like to use estimates from a multiple regression model to help prospective sellers determine a reasonable asking price for their homes. She believes that the following four factors influence the asking price (Price) of a house:
1)   The square footage of the house (SQFT)
2)   The number of bedrooms (Bed)
3)   The number of bathrooms (Bath)
4)   The lot size (LTSZ) in acres
She randomly collects online listings for 50 single-family homes. The data file is located in the Blackboard “Case Study Indiana Real Estate Data File Excel” within the Case Study folder.

Requirements and associated point values:
.
Part 2 – Estimate and interpret a multiple regression model where the asking price is the response variable and the other four factors are the explanatory variables.
The end result should be a Excel Regression Output
SUMMARY OUTPUT                  
                      
Regression Statistics                  
Multiple R                      
R Square                      
Adj. R Square                      
Standard Error                      
Observations                      
                      
ANOVA                      
    Df   SS   MS   F   Significance F  
Regression                      
Residual                      
Total                      
                      
    Coefficients   Standard Error   t Stat   P-value   Lower 95%   Upper 95%
Intercept                      
SQFT                      
Bed                      
Bath                      
LTSZ                      

Also provide the estimate model equation: Price =
A total of 40 points will be assigned to Part 2.

Part 3 – Interpret the resulting coefficient of determination.
A total of 20 points will be assigned to Part 3.

Price   SQFT   Bed   Bath   LTSZ
399900   5.026   4   4.5   0.3
375000   3.2   4   3   5
372000   3.22   5   3   5
370000   4.927   4   4   0.3
325000   3.904   3   3   1
325000   2.644   3   2.5   5
319500   5.318   3   2.5   2.5
312900   3.144   4   2.5   0.3
299900   2.8   4   3   5
294900   3.804   4   3.5   0.2
269000   3.312   5   3   1
250000   3.373   5   3.5   0.2
249900   3.46   2   2.5   0.6
244994   3.195   4   2.5   0.2
244900   2.914   3   3   0.3
239900   2.881   4   5   0.3
234900   1.772   3   2   3.6
234000   2.248   3   2.5   0.3
229900   3.12   5   2.5   0.2
219900   2.942   4   2.5   0.2
209900   3.332   4   2.5   0.2
209850   3.407   3   2.5   0.3
206900   2.092   3   2   0.3
200000   3.859   4   2   0.2
194900   3.326   4   2.5   0.1
184900   1.874   3   2   0.5
179900   1.892   3   1.5   0.7
179500   2.5   4   2.5   0.5
165000   2.435   4   2.5   0.4
159900   2.714   3   2.5   0.2
159900   1.85   3   2.5   0.5
155000   3.068   4   3.5   0.2
154900   2.484   4   2.5   0.3
152000   1.529   4   2   0.4
149900   2.876   4   2.5   0.2
148500   2.211   4   2.5   0.1
146900   1.571   3   2   0.2
145500   1.503   4   2   0.5
144900   1.656   3   2   0.5
144900   1.521   3   2   0.6
139900   1.315   3   2   0.2
137900   1.706   3   2   0.3
132900   2.121   4   2.5   0.1
129900   1.306   3   2   0.5
129736   1.402   3   2   0.5
125000   1.325   3   2   0.3
119500   1.234   3   2   0.2
110387   1.292   3   1   0.2
106699   1.36   3   1.5   0.1
102900   1.938   3   1   0.1
              
              

Answer 1

Part 2 –

The regression output is:

Regression Statistics
Multiple R	0.919402
R Square	0.8453
Adjusted R Square	0.831549
Standard Error	32685.05
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	4	2.63E+11	6.57E+10	61.47143	1.16E-17
Residual	45	4.81E+10	1.07E+09
Total	49	3.11E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	23714.63	25435.27	0.932352	0.35613	-27514.6	74943.88	-27514.6	74943.88
SQFT	44971.68	6262.365	7.18126	5.49E-09	32358.63	57584.73	32358.63	57584.73
Bed	-5028.72	7921.085	-0.63485	0.52874	-20982.6	10925.17	-20982.6	10925.17
Bath	26142.43	8917.572	2.931564	0.005285	8181.52	44103.35	8181.52	44103.35
LTSZ	25725.12	3437.085	7.484576	1.96E-09	18802.48	32647.77	18802.48	32647.77

The multiple regression model is:

Price = 23714.63 + 44971.68SQFT - 5028.72Bed + 26142.43Bath + 25725.12LTSZ

Part 3 –

The resulting coefficient of determination is 0.8453.

84.53% of the variation in price is explained by the model.