Question

In: Statistics and Probability

A realtor in Arlington, Massachusetts, is analyzing the relationship between the sale price of a home...

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= $

Solutions

Expert Solution

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


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