Question

A realtor in Arlington, Massachusetts, is analyzing the relationship between the sale price of a home (Price in $), its square footage (Sqft), the number of bedrooms (Beds), and the number of bathrooms (Baths). She collects data on 36 sales in Arlington in the first quarter of 2009 for the analysis. A portion of the data is shown in the accompanying table.

Price   Sqft   Beds   Baths
728000   2399   4   2.5
822000   2500   4   2.5
713000   2400   3   3.0
689000   2200   3   2.5
685000   2716   3   3.5
838500   3281   4   2.5
432692   1891   3   1.5
620000   2436   4   3.5
718056   2567   3   2.5
585000   1947   3   1.5
795000   3033   4   3.5
569000   3262   4   2.0
546000   1792   3   2.0
540000   1488   3   1.5
537000   2907   3   2.5
344000   1301   3   1.0
738111   2531   4   2.5
714000   2418   4   3.0
693000   2369   4   3.0
463000   1714   3   2.0
457000   1650   3   2.0
631400   2359   4   3.0
435000   1500   3   1.5
431700   1896   2   1.5
414000   1182   2   1.5
401500   1152   3   1.0
319200   1106   3   1.0
253333   896   3   1.0
475000   1590   3   2.0
375900   2275   5   1.0
620000   1675   3   2.0
459375   1590   3   2.0
534750   2147   3   3.0
247500   1022   2   1.0
247500   1099   2   1.0
307500   850   1   1.0

Estimate the model Price =  β₀ + β₁Sqft + β₂Beds + β₃Baths + ε. (Round Coefficients to 2 decimal places.)

   

b-1. Interpret the coefficient of sqft.

• For every additional square foot, the predicted price of a home increases by $102.74.

• For every additional square foot, the predicted price of a home increases by $102.74, holding number of bedrooms and bathrooms constant.

• For every additional square foot, the predicted price of a home increases by $102.74, holding square foot, number of bedrooms and bathrooms constant.

b-2. Interpret the coefficient of beds.

• For every additional bedroom, the predicted price of a home increases by $17,808.68.

• For every additional bedroom, the predicted price of a home increases by $17,808.68, holding square footage and number of baths constant.

• For every additional bedroom, the predicted price of a home increases by $17,808.68, holding square foot, number of bedrooms and bathrooms constant.

b-3. Interpret the coefficient of baths.

• For every additional bathroom, the predicted price of a home increases by $100,202.60.

• For every additional bathroom, the predicted price of a home increases by $100,202.60, holding square footage and number of bedrooms constant.

• For every additional bathroom, the predicted price of a home increases by $100,202.60, holding square foot, number of bedrooms and bathrooms constant.

c. Predict the price of a 2,188 square-foot home with four bedrooms and three bathrooms. (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

PriceˆPrice^               $

rev: 12_10_2018_QC_CS-151075, 02_21_2019_QC_CS-159957, 02_25_2019_QC_CS-160205

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Answer 1

(first part)  Price = 72968.88+ 102.74 *Sqft + 17808.68*Beds + 100202.6*Baths

(b1)For every additional square foot, the predicted price of a home increases by $102.74, holding number of bedrooms and bathrooms constant.

since the the slope for sqft is =102.74

(b2)For every additional bedroom, the predicted price of a home increases by $17,808.68, holding square footage and number of baths constant.

since the the slope for bedroom is =17,808.68

(b3)For every additional bathroom, the predicted price of a home increases by $100,202.60, holding square footage and number of bedrooms constant.

(c) square-foot=2188, bedrooms=4 and bathrooms=3, the estimated

Price = 72968.88+ 102.74 *2188 + 17808.68*4 + 100202.6*3=669604.3

following regression analysis information has been generated using ms-excel

R Square	0.78204
Adjusted R Square	0.761607
Standard Error	82740.34
Observations	36
ANOVA
	df	SS	MS	F	Significance F
Regression	3	7.86E+11	2.62E+11	38.27204	1.07E-10
Residual	32	2.19E+11	6.85E+09
Total	35	1.01E+12
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	72968.88	59610.04	1.224104	0.229849	-48452.8	194390.6
X Variable 1	102.739	38.7724	2.649798	0.012411	23.76223	181.7158
X Variable 2	17808.68	24707.26	0.720787	0.476273	-32518.4	68135.72
X Variable 3	100202.6	26991.82	3.712332	0.00078	45222.06	155183.1