The data set hprice4.raw has data on 114 homes sold in 1998 in a small town in New England. The data set contains information on the sales price of the house(variable nameprice, measured on thousands of dollars), the number of bedrooms(bedrooms), bathrooms (bathrooms), other rooms (otherrooms), square feet of livingspace (sq_feet) and age (age) of the home. Download the data with

detach(d)

url1 <- "http://www-personal.umich.edu/~hagem/data/hprice4.raw"

d1 <- read.table(url1, header=TRUE)

attach(d1)

(The detach command just removes the data set from problem 3 from the memory, incase it is still there.) Initially estimate a regression with house prices as the outcome of interest and four covariates: age in years, # of bedrooms, # of bathrooms, # of other rooms. Give a precise interpretation of the coefficient on age in years and # ofbedrooms and provide a numeric example. Now, estimate a second model and add tothe original regression the square feet of living space. What happens to the coefficienton # of bathrooms, # of bedrooms, and # of other rooms in this new model comparedto the previous one? Why have the coefficients on these three variables changed so dramatically? Interpret the coefficient on square feet of living space.