a real estate agency collected the data shown

Question

A real estate agency collected the data shown below, where

          y  = sales price of a house (in thousands of dollars)

          x₁ = home size (in hundreds of square feet)

          x₂ = rating (an overall rating for the house expressed on a scale from   1 (worst) to 10 (best).

 

                             Sales Price (y)    Home Size (x₁)        Rating (x2)    

                                    180.0                     23                           5

                                      98.1                      11                           2

                                    173.1                     20                           9

                                    136.5                     17                           3

                                    141.0                     15                           8

                                    165.9                     21                           4

                                    193.5                     24                           7

                                    127.8                     13                           6

                                    163.5                     19                           7

                                    172.5                     25                           2              

 

     The agency developed the following regression model:

                 y = β_o + β₁ x₁ + β₂ x₂+ €

     a) Show why this may be a reasonable model for the relationship between the sales price and home size? 

     b) What factors are represented in the error term in this model?  Give a specific example of these factors.