Chad Dobson has heard about the positive outlook for real estate investment in c
ID: 3438253 • Letter: C
Question
Chad Dobson has heard about the positive outlook for real estate investment in college towns. He is interested in investing in Davis, California, which houses one of the University of California campuses. He uses zillow.com to access data on 2011 monthly rent for 27 houses, along with three characteristics of the home: number of bedrooms (Beds), number of bathrooms (Baths), and square footage (Sqft). The data, shown in the accompanying table, can also be found on the text website, labeled Davis Rental.
Estimate a linear model that uses rent as the response variable. (Round your answers to 4 decimal places.)
Estimate an exponential model that uses log of rent as the response variable. (Round your answers to 4 decimal places.)
Compute the predicted rent for a 1,500-square-foot house with three bedrooms and two bathrooms for the linear and the exponential models (ignore the significance tests). (Round intermediate coefficient values to 4 decimal places and final answers to 2 decimal places.)
Use R2 to select the appropriate model for prediction.
Rent Beds Baths Sqft 2950 4 4.0 1453 2400 4 2.0 1476 2375 3 3.0 1132 2375 3 3.0 1132 2350 4 2.5 1589 2000 3 2.5 1459 1935 3 2.0 1200 1825 3 2.0 1248 1810 2 2.0 898 1735 3 2.5 1060 1695 3 2.0 1100 1405 3 1.0 1030 1375 2 1.0 924 1365 2 1.0 974 1325 2 2.0 988 1275 2 2.0 880 1200 1 1.0 712 1180 2 1.5 890 1180 2 2.0 960 1115 2 1.0 1020 1100 2 1.0 903 1060 1 1.0 724 1007 3 2.0 1260 850 2 1.5 890 810 1 1.0 570 785 1 1.0 475 744 2 1.0 930Explanation / Answer
FRom SPSS
From Excel
a1) Estimate a linear model that uses rent as the response variable.
SOl) The multiple regression equation is y=a+bx1+cx2+dx3
From excel sheet we have
Rent=65.82551 +237.8506(Beds) +389.3673 (BAths) +0.18309 (Sqft)
a2)Estimate an exponential model that uses log of rent as the response variable
Sol)
Sol) Rent= 540.5184 + 1.1418(Beds) + 1.24491(Baths) + (1.0002)Sqft
b 1)Compute the predicted rent for a 1,500-square-foot house with three bedrooms and two bathrooms for the linear and the exponential models (ignore the significance tests).
SOl) Linear
Rent=65.82551 +237.8506(Beds) +389.3673 (BAths) +0.18309 (Sqft)
when 1,500-square-foot house with three bedrooms and two bathrooms
Rent=65.82551 +237.8506(3) +389.3673 (2) +0.18309 (1500)
Rent=1832.747
Exponential
:Rent= 540.5184 + 1.1418(Beds) + 1.24491(Baths) + (1.0002)Sqft
Rent=540.5184 + 1.1418(3) + 1.24491(2) + (1.0002)1500
Rent=2046.734
C1)Compute the value of the R2, defined in terms of rent.
Sol)
Linear: R2=0.794
Exponential: R2=0.74078
C2) Use R2 to select the appropriate model for prediction.
Sol) Hence From above R2 we conclude that linear regression is best fits for the given data.
SUMMARY OUTPUT Regression Statistics Multiple R 0.890831 R Square 0.79358 Adjusted R Square 0.766656 Standard Error 284.6173 Observations 27 ANOVA df SS MS F Significance F Regression 3 7162928 2387643 29.47452 4.68E-08 Residual 23 1863161 81007 Total 26 9026089 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 65.82551 267.2604 0.246297 0.807637 -487.045 618.6958 -487.045 618.6958 Beds 237.8506 194.8622 1.220609 0.234601 -165.253 640.9537 -165.253 640.9537 Baths 389.3673 103.3422 3.767749 0.001 175.5877 603.1468 175.5877 603.1468 Sqft 0.183094 0.60568 0.302295 0.765144 -1.06985 1.436039 -1.06985 1.436039