Suppose you are a first-time home buyer. You are trying to understand why some homes are priced differenily than others. You collect data on a random sample of 10,000 homes sold in the 11.5. in the first gquarier of 2021. Then you esiimate the following model using Ordinary Least Squares (OLS): }'H':.;:f,'r.'t- = 7,000 + 200homesize; + 5 lolsize; 800 age; ADD0IT0) A; (zo0m (70) (2} [20107) (G001 R? =052 SER = 50,000 In this model, i indexes the home, price; is the selling price of home @ measured in dollars (8s), homesize; is the size of home 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 H(4; 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. (18) Write down the null and alternative hypotheses associated with the "regression F-statistic" (i.e., the statistic that tests the overall significance of the model). Suppose the regression F-statistic in this model equals 43. What do you conclude? Let o = 0.05. (5 points) (19) Test whether homesize; and lotsize; are jointly statistically significant. Write down the null and alternative hypotheses for this test. Suppose the relevant test statistic's value is 4.80. What do you conclude? Let o = 0.01. (5 points)(20) Write down the model for the "restricted regression" associated with the joint hypothesis test in (Q19). You may write the model as the population regression function since you cannot estimate it without using Stata software. (21) In general, do you think the original model in Part 3 shows the causal effect of home size on home price? Why or why not? (5 points)