Chad Dobson has heard about the positive outlook for real es

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.

Solution

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.