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
569077	1731	3	1.5
831833	2800	4	3.0
689000	2200	3	2.5
685000	2716	3	3.5
838500	3281	4	2.5
625000	2732	4	2.5
620000	2436	4	3.5
587500	2100	3	1.5
585000	1947	3	1.5
795000	3033	4	3.5
379333	2175	3	1.0
764400	2509	4	3.0
540000	1488	3	1.5
732273	3964	4	3.5
344000	1301	3	1.0
511000	1752	3	1.5
714000	2418	4	3.0
495000	1692	3	2.0
463000	1714	3	2.0
639800	2310	4	3.0
631400	2359	4	3.0
435000	1500	3	1.5
431700	1896	2	1.5
414000	1182	2	1.5
602250	1728	4	2.0
478800	1660	4	2.0
253333	896	3	1.0
285000	954	2	1.0
375900	2275	5	1.0
372000	1005	2	1.0
459375	1590	3	2.0
534750	2147	3	3.0
412500	1703	3	2.0
247500	1099	2	1.0
307500	850	1	1.0

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

	coefficients
intercept
sqft
beds
baths

b-1. Interpret the coefficient of sqft.

• For every additional square foot, the predicted price of a home increases by $107.67.

• For every additional square foot, the predicted price of a home increases by $107.67, holding number of bedrooms and bathrooms constant.

• For every additional square foot, the predicted price of a home increases by $107.67, 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 $13,699.54.

• For every additional bedroom, the predicted price of a home increases by $13,699.54, holding square footage and number of baths constant.

• For every additional bedroom, the predicted price of a home increases by $13,699.54, 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 $82,074.78.

• For every additional bathroom, the predicted price of a home increases by $82,074.78, holding square footage and number of bedrooms constant.

• For every additional bathroom, the predicted price of a home increases by $82,074.78, holding square foot, number of bedrooms and bathrooms constant.

c. Predict the price of a 2,078 square-foot home with two bedrooms and one bathrooms. (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)

price= $

Answer 1

Output:
Residuals:
    Min      1Q  Median      3Q     Max 
-148031  -42248  -12631   82774  117890 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) 111454.8    54196.9   2.056  0.04797 * 
Sqft           107.7       36.2   2.975  0.00554 **
Beds         13699.5    23008.3   0.595  0.55575   
Bath         82074.8    25782.1   3.183  0.00323 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 80150 on 32 degrees of freedom
Multiple R-squared:  0.7851,    Adjusted R-squared:  0.7649 
F-statistic: 38.97 on 3 and 32 DF,  p-value: 8.543e-11

a)

intercept	111454.8
sqft	107.67
beds	13699.54
baths	82074.78

b)1) For every additional square foot, the predicted price of a home increases by $107.67, holding number of bedrooms and bathrooms constant.

2)For every additional bedroom, the predicted price of a home increases by $13,699.54, holding square footage and number of baths constant.

3)For every additional bathroom, the predicted price of a home increases by $82,074.78, holding square footage and number of bedrooms constant.

c) Price = 111454.8 + 107.7*Sqft + 13699.5*Beds + 82074.8*Baths

Substituting the values sqft=2078;beds=2;bath=1 in the above equation we get the price =$444729