A4 Suppose the equation estimated using data is:log(rent) = .043 + .066 log(pop) + .507 log(avginc) + .0056 pctstu(.081)(.844) (.039)(.0017)n = 64, R² = .458.We would like to test the hypothesis that size of the student body relative to thepopulation has no ceteris paribus effect on monthly rents.Can you reject the hypothesis against the two-sided alternative at the 5% levels?OYes because the t statistics is above the critical value. We can reject thehypothesis HO: beta3=0.Yes because the t statistics is below the critical value. We can reject thehypothesis HO: beta3 =0.No because the tstatistics is above the critical value. We cannot reject thehypothesis HO: beta3 =0.No because the tstatistics is below the critical value. We cannot reject thehypothesis HO: beta3 =0.Question 8Using the standard normal approximation, find the 95% confidence interval forbeta3.The lower bound = Blank 1The upper bound = Blank 2Round off your answer up to 3 decimal places. (If 0.01 is the answer, you can answereither 0.01, 0.010, .01, or .010.Blank # 1Blank # 2 Question 5 (Suppose that the causal population regression model (the true model) is given by.where y is the wage, x] is the individual's education (years of education), x2 is the individual's on-the-job training,and x3 is the individual's ability.Suppose that we know the true population parameters are given as:Bo = 15, B1= 0.2, 2= 0.1, 53= 1.0You do not observe ability and run the following regression model:y = bo+ bjx+ bgx +e (2)where bo, b1 , and b, are parameters and e is the error term. As we already discussed, the error term e inEquation (2) includes B3%3 + K.Suppose you got three observations (for illustration purpose, assume that this is the population data; i.e.you are only interested in these three individuals.).Years of Education (X1)Wage (Y)On-the-job Training (X2)Error Term (e)15153010.5102010-920104020What is the sign of the bias in the estimate of 6, if you run regression without x3 ? [Blank 1]What is the sign of the bias in the estimate of ß, if you run regression without x3 ? [Blank 2]Note: Give an answer either positive or negative.Blank # 1Blank # 2

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Suppose the equation estimated using data is: log(rent) = .043 + .066 log(pop)+ .507 log(avginc) + .0056 pctstu (.081) (.844) (.039) (.0017) n = 64, R² = 458. We would like to test the hypothesis that size of the student body relative to the population has no ceteris paribus effect on monthly rents. Can you reject the hypothesis against the two-sided alternative at the 5% levels? ) Yes because the t statistics is above the critical value. We can reject the hypothesis HO: beta3=0. Yes because the t statistics is below the critical value. We can reject the hypothesis HO: beta3 =0. O No because the t statistics is above the critical value. We cannot reject the hypothesis HO: beta3 =0. No because the t statistics is below the critical value. We cannot reject the hypothesis HO: beta3 =0.