In: Statistics and Probability
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= $
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