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Consider the following linear model with Y the dependent and XL, Xz the independent variables: Y = ao + a Xu+azX25+ where i=1, 2, 3, ... n; and n refers to the total number of observations {Y, XL, X2.) for the population {Y, X., Xz); and {ao, a, az} are the model (population) parameters. The task is to use {Y, X.. X2) to estimate {ao, ai, az}: Yo = a +sX1 + a2X2 + where fo, ai, az} are the estimated model parameters, or the regression coefficients. The below are 31 observations of (Y.X.X}; i Y X1, X2; . 1 -0.07 0.80 3.18 17 0.16 0.95 3.05 2 0.06 0.93 3.17 18 -0.34 0.87 3.44 3 0.25 1.06 2.76 19 -0.04 0.86 3.02 4 -0.13 0.99 2.99 20 -0.08 0.91 2.97 5 -0.05 0.93 3.19 21 -0.22 0.81 3.69 6 0.39 0.97 2.98 22 0.02 0.99 3.02 7 -0.22 0.80 3.15 23 -0.12 0.87 3.28 8 0.11 0.90 3.07 24 0.38 0.83 2.60 9 -0.05 0.82 3.39 25 -0.42 0.95 3.24 10 0.15 1.06 3.10 0.21 1.06 3.19 11 0.09 0.92 3.11 27 0.01 0.95 3.22 12 -0.21 0.87 3.19 28 -0.28 0.93 3.41 13 0.44 0.88 2.80 14 -0.36 0.80 3.35 30 0.03 0.95 3.39 15 0.29 0.76 2.45 31 -0.01 1.03 3.36 26 29 0.08 0.82 2.54 The regression results are listed in Tables A and B below. The null hypothesis is that variables X, and X have no explanatory power to Y. Table A: The estimated coefficients. Coefficients Standard Error t-statistics Intercept 1.11 0.43 ?? X Variable 1 0.75 0.35 ?? X Variable 2 -0.58 0.10 ?? Table B: ANOVA df 2.00 Regression sum of squares Sum of Squares Errors F-statistics 0.87 0.44 ?? Regression Residual 28.00 0.69 0.02 Total 30.00 1.57 Note: Regression sum of squares = (1 7)', and Sum of Squares Errors = {(Y; - Y1)? Answer the following questions: a. (10%) What are the 6 basic assumptions for estimating linear regression models? What is the economic meaning of the estimated coefficient, az? Why is it important to generally include ao in the linear model? b. (8%) What are the 3 t-statistics in Table A, and the F-statistics in Table B? C. (8%) Comment on the hypothesis test results in b), assuming 5% significant level

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