Question

A statistical program is recommended.

Spring is a peak time for selling houses. Suppose the data below contains the selling price, number of bathrooms, square footage, and number of bedrooms of 26 homes sold in Ft. Thomas, Kentucky, in spring 2018.

Selling Price	Baths	Sq Ft	Beds
160,000	1.5	1,786	3
170,000	2	1,768	3
178,000	1	1,219	3
182,500	1	1,578	2
195,100	1.5	1,125	4
212,500	2	1,196	2
245,900	2	2,128	3
250,000	3	1,280	3
255,000	2	1,596	3
258,000	2.5	2,374	4
267,000	2.5	2,439	3
268,000	2	1,470	4
275,000	2	1,688	4

Selling Price	Baths	Sq Ft	Beds
295,000	2.5	1,860	3
325,000	3	2,056	4
325,000	3.5	2,776	4
328,400	2	1,408	4
331,000	1.5	1,972	3
344,500	2.5	1,736	3
365,000	2.5	1,990	4
385,000	2.5	3,640	4
395,000	2.5	1,928	4
399,000	2	2,108	3
430,000	2	2,462	4
430,000	2	2,615	4
454,000	3.5	3,700	4

Consider the estimated regression equation we developed that can be used to predict the selling price given the number of bathrooms, square footage, and number of bedrooms in the house.

(x₁ denotes number of bathrooms, x₂ denotes square footage, x₃ denotes number of bedrooms, and y denotes the selling price.)

ŷ = −1770.46 + 18130.69x₁ + 60.00x₂ + 40706.14x₃

(a)

Does the estimated regression equation provide a good fit to the data? Explain. (Round your answer to two decimal places.)

Since the adjusted R²= _____

(b)

Consider the estimated regression equation that was developed which predicts selling price given the square footage and number of bedrooms.

(x₂ denotes square footage,  x₃ denotes number of bedrooms, and y denotes the selling price.)

ŷ = 7679.47 + 67.88x₂ + 44959.40x₃

Compare the fit for this simpler model to that of the model that also includes number of bathrooms as an independent variable. (Round your answer to Three decimal places.)

The adjusted R² for the simpler model is:_____

Answer 1

a) With X1, X2, X3

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.731959402
R Square	0.535764566
Adjusted R Square	0.472459735
Standard Error	63051.30679
Observations	26
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1.00936E+11	33645370273	8.463249182	0.000632515
Residual	22	87460280335	3975467288
Total	25	1.88396E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1770.455048	70253.81669	-0.025200838	0.980121962	-147467.9534	143927.0433	-147467.9534	143927.0433
Baths	18130.69307	24766.70749	0.732059079	0.471859809	-33232.31458	69493.70072	-33232.31458	69493.70072
Sq Ft	59.99529962	23.63299424	2.538624561	0.018715141	10.98346935	109.0071299	10.98346935	109.0071299
Beds	40706.13783	22399.92992	1.817243981	0.082827556	-5748.473551	87160.74921	-5748.473551	87160.74921

ŷ = −1770.46 + 18130.69x1 + 60.00x2 + 40706.14x3

x1 denotes number of bathrooms,

x2 denotes square footage,

x3 denotes number of bedrooms,

and y denotes the selling price.

Adjusted R^2 = 0.47, it is close to 0.5, which means not a good fit, it is moderate fit

b) With X2, X3

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.724193339
R Square	0.524455992
Adjusted R Square	0.483104339
Standard Error	62411.94666
Observations	26
ANOVA
	df	SS	MS	F	Significance F
Regression	2	98805616177	49402808088	12.68283019	0.000193952
Residual	23	89590774977	3895251086
Total	25	1.88396E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	7679.466794	68357.42325	0.112342836	0.911526323	-133728.637	149087.5706	-133728.637	149087.5706
Sq Ft	67.88020883	20.82253767	3.259939298	0.003446639	24.80550782	110.9549098	24.80550782	110.9549098
Beds	44959.40208	21413.95612	2.099537415	0.046942019	661.2587841	89257.54538	661.2587841	89257.54538

ŷ = 7679.47 + 67.88x2 + 44959.40x3

x2 denotes square footage,

x3 denotes number of bedrooms,

and y denotes the selling price.

Adjusted R^2 = 0.48

Adjusted R^2 simpler model > Adjusted R^2 from part a, So model from part b is preferred  

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