A realtor examines the factors that influence the price of a house. He collects

Question

A realtor examines the factors that influence the price of a house. He collects data on the prices for 36 single-family homes in Arlington, Massachusetts sold in the first quarter of 2009. For explanatory variables, he uses the house’s square footage (Sqft), as well as its number of bedrooms (Beds) and bathrooms (Baths). The data are shown in the accompanying table.

I was able to calculate the linear regression model, but I am not sure how to calculate the exponential model through excel. Please provide instructions for your work :)

A realtor examines the factors that influence the price of a house. He collects data on the prices for 36 single-family homes in Arlington, Massachusetts sold in the first quarter of 2009. For explanatory variables, he uses the house’s square footage (Sqft), as well as its number of bedrooms (Beds) and bathrooms (Baths). The data are shown in the accompanying table.

2 d ll bl 550550555550055050000055500000000000 32323223112221221222221111121-11211- 44333344333433343333333223443523233- a Sat 2222222227427491226165588 52 3 3 2 2 5 2 1 2 6 $50 e 80006426074228712724050622342552 a Ne 527 42188422888644311196553310988776 3 887666665555555555444444443333333333

Explanation / Answer

for exponential model the model is assumed to be

price=alpha0*alpha1sqft*alpha2beds*alpha3baths

so after taking log on both sides

ln(price)=ln(alpha0)+ln(alpha1)*sqft+ln(alpha2)*beds+ln(alpha3)*baths

the above model is linear in parameters

so the regression model is assumed to be

ln(price)=beta0+beta1*sqft+beta2*beds+beta3*baths+e beta0=ln(alpha0) beta1=ln(alpha1) beta2=ln(alpha2) beta3=ln(alpha3)

now using excel we get the model as

ln(price)=12.4+0.000199*sqft+0.0002*beds+0.169*baths

so answer of

a-2) ln(price)=12.4000+0.0002*sqft+0.0002*beds+0.169*baths

so the actual model becomes

price=12.4*(0.0002)sqft*(0.0002)beds*(0.169)baths

b-2) so if sqft is increases by one unit

then pricenew=12.4*(0.0002)sqft+1*(0.0002)beds*(0.169)baths=0.0002*price

so new price is decreased by (1-0.0002)*100=99.98% [answer]

similarly if no. of beds increased by 1 then

pricenew=12.4*(0.0002)sqft*(0.0002)beds+1*(0.169)baths=0.0002*price

so new price is decreased by (1- 0.0002)*100=99.98% [answer]

similarly if no. of bathrooms increased by 1 unit

pricenew=0.169*price

so new price is decreased by (1-0.169)*100=83.1% [answer]

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