Question 1 Considertheslmple linear regression model: Yr = 15':- +513: +ur. 1' = 1.....10. MEI-131 his = E93.E}=\"1X.: = 4122:1314? = 293 Eli-L311? = 143. and 3331 1'5 = 2141. Additionally, from the results of the regression we know that 2:3le = 90.042. a] State the problem of minimizing the square of errors. Then solve the minimization problem in order to obtain the following formula [20 Marks] 1\"; , \"21m; It? 'EEe'ri' '\" ii b] Use the formula above to compute the ordinary least squares [OLS] estimate of .31. [5 Marks] c] State the formula to calculate the standard error of the ll'Zl'LS estimate of #1 if the error terms are homoskedastic and then compute the standard error of 31. Lil =- [10 Marks] d] Is 31 statistically significant at 5% level? Calculate the 99% condence interval for 51. If you think that there is not enough information to answer please state which infcrrnation is needed in order to do so. [to Marks] a] Comment on the reliability of 0L5 estimators in this regression model. [5 Marks] Question 2 Consider the following estimated regression model [standard errors are in parentheses}: = 4.93 + c.5321: 4-12th {2.1a} {one} {1.9a} t=*I,...,54:'R2 = use, ovv = 2.412 a} Test it there is autocorrelation in this model or not? If you think that there is not enough information to answer please state which information is needed in order to do so. [to Marks] b] Test the overall significance of the model. If you think that there is not enough information to answer please state which information is needed in order to do so. [15 Marks] o] What assumptions are required to be able to use this regression analysis for statistical inference. [to Marks] d] Suppose that. by mistake. you consider the following model fit = $0 + 31K\" + at and you omit the variable 22:. State the formula which shows the expected value of 31 when there is an omitted variable. Discuss when the omitted variable bias is different from zero. Let the variance of Xi be 5.15, the variance of 1:2 be 3.45, and the covariance between x1 and X2 be 2.35. Determine whether the regression with the omitted variable will overestimate or underestimate the real value of the parameter 31. [15 Marks]