Suppose you are a first-time home buyer. You are trying to understand why some homes are priced differently than others. You collect data on a random sample of 10,000 homes sold in the U.S. in the first quarter of 2021. Then you estimate the following model using Ordinary Least Squares (OLS): price; = 7,000 + 200homesize; + 5 lolsize; - 800age; - 4000HOA; (2,000) (70) (2) (200) (600) R' = 0.52 SER = 50, 000 In this model, i indexes the home, price, is the selling price of home i measured in dollars ($s), homesize; is the size of home i measured in square feet, lolsize; is the size of home i's lot (i.e., land) measured in square feet, age; is the age of home i measured in years, and HOA; is a binary variable that equals 1 if there is a "home ownership association fee" attached to the home, and equals 0 otherwise. Heteroskedasticity-robust standard errors appear in parentheses. (15) Interpret B1 in a sentence. (5 points) (16) What is the predicted price for a house that is 2000 square feet, on a lot size of 5000 square feet, that is 50 years old, and does not have a HOA fee? (5 points)(17) Suppose you are told that the lot size measurement equals the home size plus surrounding land on the plot for every house in the sample. What would this imply about the presence of perfect or imperfect multicollinearity in the model as written? (5 points)