3. Give the population model Yi = β0 + β1Xi + ui T
he variance of β1 will (BLANK) as the variation in x decreases, and it will decrease if we (BLANK) the variance of the error term.
a) increase. increase b) increase. decrease c) decrease. decrease d) decrease. increase
3. Give the population model Yi = β0 + β1Xi + ui T he variance of...
Consider the linear regression model Yi = β0 + β1 Xi + ui Yi is the ______________, the ______________ or simply the ______________. Xi is the ______________, the ______________ or simply the ______________. is the population regression line, or the population regression function. There are two ______________ in the function (β0 & β1 ). β0 is is the ______________ of the population regression line; β1is is the ______________ of the population regression line; and ui is the ______________. A. Coefficients...
Now consider the following two models: Yi = β0 + β1Xi + ui (M1) Yi = β0 + β1Xi + β2X2 i + ui (M2) 1 and determine whether each of the following statements is true, false or uncertain, and explain why: a) M1 has better out-of-sample fit than M2 b) The R2 will be higher for M1 than for M2 c) M2 and M1 are nested models d) I can test whether M1 and M2 are statistically different by...
Consider the linear model: Yi = α0 + α1(Xi − X̄) + ui. Find the OLS estimators of α0 and α1. Compare with the OLS estimators of β0 and β1 in the standard model discussed in class (Yi = β0 + β1Xi + ui). Consider the linear model: Yį = ao + Q1(X; - X) + Ui. Find the OLS estimators of do and a1. Compare with the OLS estimators of Bo and B1 in the standard model discussed in...
Suppose that we have data on ECON 333 test scores (Yi), duration for which student i studies for exam (Xi), and the major of the student, call it Di, where Di =( 1, if economics major 0, if non economics major Consider the following model: Yi = β0 + β1Xi + β2Di + β3DiXi + ui (1) where Assumption 1 holds: E (ui|Xi,Di) = 0. (2) Yi is the score between 0 and 100. Xi is the duration studied in...
Consider the regression model: yi = β0 + β1Xi + εi for…. i = 1 Where the dummy variable (0 = failure and 1 = success). Suppose that the data set contains n1 failure and n2 successes (and that n1+n2 = n) Obtain the X^T(X) matrix Obtain the X^T(Y) matrix Obtain the least square estimate b
Consider the model yi = β0 +β1X1i +β2X2i +ui . We fail to reject the null hypothesis H0 : β1 = 0 and β2 = 0 at 5% when: a) A F test of H0 : β1 = 0 and β2 = 0 give us a p value of 0.001 b) A t test of H0 : β1 = 0 give us a p value of 0.06 and a t test of H0 : β2 = 0 a p value...
Consider a population linear regression model: Yt=β0 + β1Xt + ut Calculate: 1. Variance 2. Covariance of ut and Xt 3. β0 4. β1
Question 3 If data is missing for completely random reasons (i.e., not related to X or Y), then this leads to: Question 3 options: A bias in the OLS estimator. A reduction in sample size. An increase in the variance of the OLS estimator. Both (b) and (c). Question 4 Consider the linear probability model Yi = β0 + β1Xi + ui. Assume E(ui|Xi)=0. Which of the following statements are true? Question 4 options: The predicted value of the dependent...
Testing the equality of two regression coefficients. Suppose that you are given the following regression model: Yi = β1 + β2X2i + β3X3i + ui and you want to test the hypothesis that β2 = β3. If we assume that the ui are normally distributed, it can be shown that t = βˆ 2 − βˆ 3 var (βˆ 2) + var (βˆ 3) − 2 cov (βˆ 2, βˆ 3) follows the t distribution with n − 3...