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1. Consider the following multiple regression models Y βι + β2 X2i + β3 X3i + ui (1) Population r...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i = 1, 2, ...,n, where B1, B2 and Bzare population parameters and the Ui are IID (0,02). Note that: Y; routput, X2i =labor input, Xzi =capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Yį = B2X2 X : exp(ui) to a linear model (b) How do you the interpret B2? (c) How do you the interpret By?...
Q. 1 Consider the multiple linear regression model Y = x3 + €, where e indep...
Q. 1 Consider the multiple linear regression model Y = x3 + €, where e indep MV N(0,0²V) and V +In is a diagonal matrix. a) Derive the weighted least squares estimator for B, i.e., Owls. b) Show Bwis is an unbiased estimator for B. c) Derive the variances of w ls and the OLS estimator of 8. Is the OLS estimator of still the BLUE? In one sentence, explain why or why not.
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0...
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0 and β2-β3 and β5-1 Rewrite the null hypothesis Ho in the form of RB-r using the matrix R and two vectors B and r b. (5) Consider the following wage regression result: log(wage) 3.240.06educ 0.51Female 0.01educ Female, where educ denotes years of education and Female is a dummy variable for females. What is the return to schooling for male workers? What is the return...
Question 12 3 pts Consider the estimated multiple regression model using OLS, with the standard errors...
Question 12 3 pts Consider the estimated multiple regression model using OLS, with the standard errors in parentheses below each estimated coefficient. There are 1,576 observations in the sample: Ỹ = 10 + 2x - 5X36 (3) (1.5) (2) Suppose the null hypothesis is that the true coefficient (population parameter) for X3 is equal to 1. The test statistic associated with this null hypothesis is: -3 0-2 O 2
Question 4 3 pts Consider the estimated multiple regression model using OLS, with the standard errors...
Question 4 3 pts Consider the estimated multiple regression model using OLS, with the standard errors in parentheses below each estimated coefficient. There are 1,576 observations in the sample: Y = 10 + 2X2i - 5Xzi (3) (1.5) (2) Suppose that the sample mean of Y is 30. For the 18th observation (i=18) in the sample, the value of X2 is 50, the value of X3 is 16, and the value of Y is 20. The residual associated with the...
Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo +...
Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo + B1Xil +...+Bkxik + Ui estimated by OLS/MOM. Let the estimators beßo, Ŝ1,..., ØK. Question 1 (1 point) The p-value for undertaking a hypothesis test is the smallest significance level for which we reject a null hypothesis that is correct. True False Question 2 (1 point) To test Ho: B3 = 34 vs H1 : B3 – B4 > 0, we form the test statistic...
Question 1 Consider the following Multiple Regression Model yı BoB1B2 + El, y2 BIB2E2 y3 B2Es,...
Question 1 Consider the following Multiple Regression Model yı BoB1B2 + El, y2 BIB2E2 y3 B2Es, and y4 Bo+BI4 Suppose that & 's are independent and identically distributed N(0, o2 ) a) Write down the model in the matrix form b) Show that 2 2 1 X'X2 3 2 1.67 -1.33 0.33 (X'X) 1.67 Note that -1.33 -0.67 1 2 3 0.33 -0.67 0.67 c) Find unbiased estimators for Bo, Bi, and B2 given that y 3, y2 1, y3-...
1. In order to test whether the multiple linear regression model y bo +b,x1 + b2X2 is better than the average model (lazy model), which of the following null hypotheses is correct: a. Ho' b1...
1. In order to test whether the multiple linear regression model y bo +b,x1 + b2X2 is better than the average model (lazy model), which of the following null hypotheses is correct: a. Ho' b1 = b2 = 0 Но: B1 B2-0 с. We have a dataset Company with three variables: Sales, employees and stores. To build a multiple linear regression model using Sales as dependent variable, number of stores and number of employees as independent variables, which of the...
1. For each of the following regression models, write down the X matrix and 3 vector....
1. For each of the following regression models, write down the X matrix and 3 vector. Assume in both cases that there are four observations (a) Y BoB1X1 + B2X1X2 (b) log Y Bo B1XiB2X2+ 2. For each of the following regression models, write down the X matrix and vector. Assume in both cases that there are five observations. (a) YB1XB2X2+BXE (b) VYBoB, X,a +2 log10 X2+E regression model never reduces R2, why 3. If adding predictor variables to a...
Q2. Suppose you are given the following Cob-Douglas Production Y; = B1X2 X3 exp(ui) for i = 1, 2, ...,n, where B1, B2 and Bzare population parameters and the Ui are IID (0,02). Note that: Y; routput, X2i =labor input, Xzi =capital input, exp = base of the natural logarithm. (a) Transform the above non-linear model, Yį = B2X2 X : exp(ui) to a linear model (b) How do you the interpret B2? (c) How do you the interpret By?...
Q. 1 Consider the multiple linear regression model Y = x3 + €, where e indep MV N(0,0²V) and V +In is a diagonal matrix. a) Derive the weighted least squares estimator for B, i.e., Owls. b) Show Bwis is an unbiased estimator for B. c) Derive the variances of w ls and the OLS estimator of 8. Is the OLS estimator of still the BLUE? In one sentence, explain why or why not.
a. (5) From the multiple regression model we want to test the following hypothesis: Ho: β1-0 and β2-β3 and β5-1 Rewrite the null hypothesis Ho in the form of RB-r using the matrix R and two vectors B and r b. (5) Consider the following wage regression result: log(wage) 3.240.06educ 0.51Female 0.01educ Female, where educ denotes years of education and Female is a dummy variable for females. What is the return to schooling for male workers? What is the return...
Question 12 3 pts Consider the estimated multiple regression model using OLS, with the standard errors in parentheses below each estimated coefficient. There are 1,576 observations in the sample: Ỹ = 10 + 2x - 5X36 (3) (1.5) (2) Suppose the null hypothesis is that the true coefficient (population parameter) for X3 is equal to 1. The test statistic associated with this null hypothesis is: -3 0-2 O 2
Question 4 3 pts Consider the estimated multiple regression model using OLS, with the standard errors in parentheses below each estimated coefficient. There are 1,576 observations in the sample: Y = 10 + 2X2i - 5Xzi (3) (1.5) (2) Suppose that the sample mean of Y is 30. For the 18th observation (i=18) in the sample, the value of X2 is 50, the value of X3 is 16, and the value of Y is 20. The residual associated with the...
Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo + B1Xil +...+Bkxik + Ui estimated by OLS/MOM. Let the estimators beßo, Ŝ1,..., ØK. Question 1 (1 point) The p-value for undertaking a hypothesis test is the smallest significance level for which we reject a null hypothesis that is correct. True False Question 2 (1 point) To test Ho: B3 = 34 vs H1 : B3 – B4 > 0, we form the test statistic...
Question 1 Consider the following Multiple Regression Model yı BoB1B2 + El, y2 BIB2E2 y3 B2Es, and y4 Bo+BI4 Suppose that & 's are independent and identically distributed N(0, o2 ) a) Write down the model in the matrix form b) Show that 2 2 1 X'X2 3 2 1.67 -1.33 0.33 (X'X) 1.67 Note that -1.33 -0.67 1 2 3 0.33 -0.67 0.67 c) Find unbiased estimators for Bo, Bi, and B2 given that y 3, y2 1, y3-...
1. In order to test whether the multiple linear regression model y bo +b,x1 + b2X2 is better than the average model (lazy model), which of the following null hypotheses is correct: a. Ho' b1 = b2 = 0 Но: B1 B2-0 с. We have a dataset Company with three variables: Sales, employees and stores. To build a multiple linear regression model using Sales as dependent variable, number of stores and number of employees as independent variables, which of the...
1. For each of the following regression models, write down the X matrix and 3 vector. Assume in both cases that there are four observations (a) Y BoB1X1 + B2X1X2 (b) log Y Bo B1XiB2X2+ 2. For each of the following regression models, write down the X matrix and vector. Assume in both cases that there are five observations. (a) YB1XB2X2+BXE (b) VYBoB, X,a +2 log10 X2+E regression model never reduces R2, why 3. If adding predictor variables to a...
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