True or False: Given the necessary assumption: E(u|X) = 0, β ̂ is a random variable...
True or False:
Given the necessary assumption: E(u|X) = 0, β ̂ is a random variable with a distribution centered at 0.
Given the necessary assumption: E(u|X) =0, β ̂ is a random variable with a distribution centered at β.
Adding more independent variables to a model will only increase R2 if they provide meaningful variation.
Adj R2 measures the proportion of the variation in the dependent variable that has been explained by the variation in the independent variable.
If cov(u,X) ≠ 0 then it is impossible for the OLS estimate β ̂ to close to the true β.
If cov(u,X) = 0 then it is very likely for the OLS estimate β ̂ to close to the true β.
My answers are true, true, false, true, true (unsure about this one), and true
Homework Answers
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True or False:
Given the necessary assumption: E(u|X) = 0, β ̂ is a random
variable...
7. True/False a. If Cov(x,u)>0, then the OLS estimator βι will then to be higher than...
7. True/False a. If Cov(x,u)>0, then the OLS estimator βι will then to be higher than β b. Suppose you run a regression and obtain the estimate B1 - 3.4. Stata tells you that the test statistic for the null hypothesis that B12 is equal to 2. This implies that the standard error of the slope coefficient is also equal to 2.
Problem 1. Let X be a normal random variable with mean 0 and variance 1 and...
Problem 1. Let X be a normal random variable with mean 0 and variance 1 and let Y be uniform(0.1) with X and Y being independent. Let U-X + Y and V = X-Y. For this problem recall the density for a normal random variable is 2πσ2 (a) Find the joint distribution of U and V (b) Find the marginal distributions of U and V (c) Find Cov(U, V).
5. Let us assume that X is non-random. Consider Y = XB+U with E(U) = 0...
5. Let us assume that X is non-random. Consider Y = XB+U with E(U) = 0 and E (UU') = 0282. Assume that N2 is known. Let Bols be the OLS estimator and Bals be the GLS estimator. (a) Compute cov (Bals, Bols). (b) Let ûOLS = Y - XBols. Compute E (ÛOLSỮOLS).
You are given that the random variable X is exponential with a mean of 1, and...
You are given that the random variable X is exponential with a mean of 1, and that the random variable Y is uniformly distributed on the interval (0, 1). Furthermore, it is known that X and Y are independent. Find the density of the joint distribution of U = XY and V = X/Y.
3. A random variable X is said to have a Cauchy(α, β) distribution if and only...
3. A random variable X is said to have a Cauchy(α, β) distribution if and only if it has PDF function Now, suppose that Xi and X2 are independent Cauchy(0, 1) random variables, and let Y = X1 + X2. Use the transformation technique to find and identify the distribution of Y by first finding the joint distribution of Xi and Y. (Seahin 3 4
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square...
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
1. Let X and Y be two random variables.Then Var(X+Y)=Var(X)+Var(Y)+2Couv(X,Y). True False 2. Let c be...
1. Let X and Y be two random variables.Then Var(X+Y)=Var(X)+Var(Y)+2Couv(X,Y). True False 2. Let c be a constant.Then Var(c)=c^2. True False 3. Knowing that a university has the following units/campuses: A, B , the medical school in another City. You are interested to know on average how many hours per week the university students spend doing homework. You go to A campus and randomly survey students walking to classes for one day. Then,this is a random sample representing the entire...
5.1 Let U a in f(X;0) ae then E(U)=0. O TRUE O FALSE 5.2 Let X1,...
5.1 Let U a in f(X;0) ae then E(U)=0. O TRUE O FALSE 5.2 Let X1, ..., X. * N (14.0). If o’ is unknown and we want to derive a confidence interval for the true population mean, then distribution of the appropriate pivotal quantity is Chi-Square with n degrees of freedom. O TRUE O FALSE Q5.3 1 Point 5.3 Let X.....X.1080). Assume both i and o? are unknown. Then the MLE of a' is unbiased, O TRUE O FALSE...
1. In simple linear regression analysis, we assume that the variance of the independent variable (X)...
1. In simple linear regression analysis, we assume that the variance of the independent variable (X) is equal to the variance of the dependent variable (Y) True False 2. The standard deviation of the sampling distribution of the sample mean is the same as the population standard deviation. True False 3. If n=20 and p=.4, then the mean of the binomial distribution is 8 True False 4. If a population is known to be normally distributed, then it follows that...
R2 be a random variable with E(X) u = (1, #2)T, let Q [0, 2] be...
R2 be a random variable with E(X) u = (1, #2)T, let Q [0, 2] be 2. (10 marks) Let X a г row vector and let Ги Гі2 T21 I22. E((X-)(X -)T) r (a) Compute E(QX) and write your answer in terms of the elements of u and (5 marks) Г. (b) Compute the variance of QX and write your answer in terms of the elements of u and Г. (5 marks)
R2 be a random variable with E(X)...
7. True/False a. If Cov(x,u)>0, then the OLS estimator βι will then to be higher than β b. Suppose you run a regression and obtain the estimate B1 - 3.4. Stata tells you that the test statistic for the null hypothesis that B12 is equal to 2. This implies that the standard error of the slope coefficient is also equal to 2.
Problem 1. Let X be a normal random variable with mean 0 and variance 1 and let Y be uniform(0.1) with X and Y being independent. Let U-X + Y and V = X-Y. For this problem recall the density for a normal random variable is 2πσ2 (a) Find the joint distribution of U and V (b) Find the marginal distributions of U and V (c) Find Cov(U, V).
5. Let us assume that X is non-random. Consider Y = XB+U with E(U) = 0 and E (UU') = 0282. Assume that N2 is known. Let Bols be the OLS estimator and Bals be the GLS estimator. (a) Compute cov (Bals, Bols). (b) Let ûOLS = Y - XBols. Compute E (ÛOLSỮOLS).
3. A random variable X is said to have a Cauchy(α, β) distribution if and only if it has PDF function Now, suppose that Xi and X2 are independent Cauchy(0, 1) random variables, and let Y = X1 + X2. Use the transformation technique to find and identify the distribution of Y by first finding the joint distribution of Xi and Y. (Seahin 3 4
1. Suppose the true conditional mean function is but by mistake, a researcher ran least square regression without the X term as in Assume cou (Xi, U)-0, E Xil]-o and E [x?]-: i. Is his/her estimate consistent for β? If not, show which OLS assumption fails and discuss potential solutions. 2. Assume the structural equation is where E [111x,-0. It was discovered that we observe Xi with a measurement error wi instead of the real value Xi It is known...
5.1 Let U a in f(X;0) ae then E(U)=0. O TRUE O FALSE 5.2 Let X1, ..., X. * N (14.0). If o’ is unknown and we want to derive a confidence interval for the true population mean, then distribution of the appropriate pivotal quantity is Chi-Square with n degrees of freedom. O TRUE O FALSE Q5.3 1 Point 5.3 Let X.....X.1080). Assume both i and o? are unknown. Then the MLE of a' is unbiased, O TRUE O FALSE...
R2 be a random variable with E(X) u = (1, #2)T, let Q [0, 2] be 2. (10 marks) Let X a г row vector and let Ги Гі2 T21 I22. E((X-)(X -)T) r (a) Compute E(QX) and write your answer in terms of the elements of u and (5 marks) Г. (b) Compute the variance of QX and write your answer in terms of the elements of u and Г. (5 marks)
R2 be a random variable with E(X)...
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