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![a) FOR ZERO CONDITIONAL MEAN tſuline) = 0 us incaxe Esine xeline] to ince {eline Given that Eſeline- inc (0) 0 700 conditiona](http://img.homeworklib.com/questions/956c1440-aba5-11eb-a5a2-2df98b7d6c62.png?x-oss-process=image/resize,w_560)
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Suppose assumptions SLR.1-SLR.3 are satisfied and consider a regression model of savings (sav) on income (inc):...
Consider the following simple regression model: a. Suppose that OLS assumptions 1 to 4 hold true. We know that homoskedasticity assumption is statedas: Var[UjIx] = σ2 for all i Now, suppose that...
Consider the following simple regression model: a. Suppose that OLS assumptions 1 to 4 hold true. We know that homoskedasticity assumption is statedas: Var[UjIx] = σ2 for all i Now, suppose that homoskedasticity does not hold. Mathematically, this is expressed as In other words, the subscript i in σ12 means that the conditional variance of errors for each individual i is different. Under heteroskedasticity, we can derive the expression for the variance of Var(B) as SST Where SSTx is the...
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume th...
a,b,c,d
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume that the true model satisfies all five standard assumptions of a simple regression model discussed in class. (a) Does the regression model we are running satisfy the zero conditional mean assumption? (b) Find the expected value of A (given X values). (e) Does the regression model we are running satisfy homoscedasticity? d) Find the variance of pi (given X...
Consider the regression model: Y = Bo + B,X+u Which of the following assumptions would, if...
Consider the regression model: Y = Bo + B,X+u Which of the following assumptions would, if not satisfied, lead to a biased estimate of Bo and B? OE(u|X)=0 o untok- var (44)=o?, for all i Ou~ N(0,0%)
Model Assumptions: Question: • Assumption MLR.1 (Linear in the Parameters): The model in the population can...
Model Assumptions:
Question:
• Assumption MLR.1 (Linear in the Parameters): The model in the population can be written as y = Bo + B1X + ... + BkXk+u where Bo, B1, ..., Bk are the unknown parameters of interest and u unobserved random error. Assumption MLR.2 (Random Sampling): We have a random samp n observations, {(Xi1, X12, ..., Xik, Yi) : 1 = 1,2,...,n}, following the population model in Assumption MLR.1. Assumption MLR.3 (No Perfect Collinearity): In the sample, none...
1. In the simple regression model y = + β1x + u, suppose that E (u)...
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
4. The Gauss-Markov Theorem says that when Assumptions 1-5 of the linear regression model are satisfied:...
4. The Gauss-Markov Theorem says that when Assumptions 1-5 of the linear regression model are satisfied: (a) The least squares estimator is unbiased (b) The least squares estimator has the smallest variance of all linear estimators (c) The least squares estimator has an approximately normal sampling distribution (d) The least squares estimator is consistent (e) None of the above
7. In a simple regression model, suppose all of the assumptions of the classical linear regression...
7. In a simple regression model, suppose all of the assumptions of the classical linear regression morel apply, except that rather than assume E (ui | Xi) = 0, you assume that E (Ui / X;) = ali and E (xi) = 0 where a > 0 is a constant. (a) What is the conditional expectation of the OLS slope coefficient, i.e. E (B1 | 21, ..., XN)? (b) In this case, is ß1 an unbiased estimator of B1 or...
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming...
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming a conditional variance function Varux=σ2h(x). Which of the following statements is correct? A) The function h(x) does not need to be estimated as part of the procedure B) If the assumption about the conditional variance of the error term is incorrect, then FWLS is still consistent. C) FWLS is the best linear unbiased estimator when there is heteroscedasticity. D) None of the above answers...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
Consider the following simple regression model: a. Suppose that OLS assumptions 1 to 4 hold true. We know that homoskedasticity assumption is statedas: Var[UjIx] = σ2 for all i Now, suppose that homoskedasticity does not hold. Mathematically, this is expressed as In other words, the subscript i in σ12 means that the conditional variance of errors for each individual i is different. Under heteroskedasticity, we can derive the expression for the variance of Var(B) as SST Where SSTx is the...
a,b,c,d
4. Suppose we run a regression model Y = β0+AX+U when the true model is Y-a0+ α1X2 + V. Assume that the true model satisfies all five standard assumptions of a simple regression model discussed in class. (a) Does the regression model we are running satisfy the zero conditional mean assumption? (b) Find the expected value of A (given X values). (e) Does the regression model we are running satisfy homoscedasticity? d) Find the variance of pi (given X...
Consider the regression model: Y = Bo + B,X+u Which of the following assumptions would, if not satisfied, lead to a biased estimate of Bo and B? OE(u|X)=0 o untok- var (44)=o?, for all i Ou~ N(0,0%)
Model Assumptions:
Question:
• Assumption MLR.1 (Linear in the Parameters): The model in the population can be written as y = Bo + B1X + ... + BkXk+u where Bo, B1, ..., Bk are the unknown parameters of interest and u unobserved random error. Assumption MLR.2 (Random Sampling): We have a random samp n observations, {(Xi1, X12, ..., Xik, Yi) : 1 = 1,2,...,n}, following the population model in Assumption MLR.1. Assumption MLR.3 (No Perfect Collinearity): In the sample, none...
1. In the simple regression model y = + β1x + u, suppose that E (u) 0. Letting oo-E(u), show that the model can always be rewrit ten with the same slope, but a new intercept and error, where the new error has a zero expected value 2. The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, nfan birth weight in ounces (bught), and an explanatory variable,...
4. The Gauss-Markov Theorem says that when Assumptions 1-5 of the linear regression model are satisfied: (a) The least squares estimator is unbiased (b) The least squares estimator has the smallest variance of all linear estimators (c) The least squares estimator has an approximately normal sampling distribution (d) The least squares estimator is consistent (e) None of the above
7. In a simple regression model, suppose all of the assumptions of the classical linear regression morel apply, except that rather than assume E (ui | Xi) = 0, you assume that E (Ui / X;) = ali and E (xi) = 0 where a > 0 is a constant. (a) What is the conditional expectation of the OLS slope coefficient, i.e. E (B1 | 21, ..., XN)? (b) In this case, is ß1 an unbiased estimator of B1 or...
QUESTION 1 Consider the following OLS regression line (or sample regression function): wage =-2.10+ 0.50 educ (1), where wage is hourly wage, measured in dollars, and educ years of formal education. According to (1), a person with no education has a predicted hourly wage of [wagehat] dollars. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing...
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