Consider a population linear regression model:
Yt=β0 + β1Xt + ut
Calculate:
1. Variance
2. Covariance of ut and Xt
3. β0
4. β1
Consider a population linear regression model: Yt=β0 + β1Xt + ut Calculate: 1. Variance 2. Covariance...
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
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...
(Do this problem without using R) Consider the simple linear regression model y =β0 + β1x + ε, where the errors are independent and normally distributed, with mean zero and constant variance σ2. Suppose we observe 4 observations x = (1, 1, −1, −1) and y = (5, 3, 4, 0). (a) Fit the simple linear regression model to this data and report the fitted regression line. (b) Carry out a test of hypotheses using α = 0.05 to determine...
Consider the model defined by, Yt = BO + B1 Yt-1 + B2 Xt + Ut. Compute the long-run coefficients (2 decimals) for the model: Short-Run Long-Run BO 1.38 B1 0.60 B2 -5.26
Consider the following regression equation: Yt = β0 + β1X1+…+ βk Xk + ut. In which of the following cases is the dependent variable binary? (a) The variable Ytindicates the gross domestic product of a country (b) The variable Ytindicates whether an adult is employed (c) The variable Ytindicates household consumption expenditure (d) The variable Ytindicates the number of children in a family
1. (20 points) Consider the linear regression model y = a + Bt + ut, ut id(0,%), (t = 1, ...,T). An estimator of B is b=1-1 YT- 41 (a) is estimator b consistent? (Hint: use Chebyshev's inequality) (b) If u i.i.d. N(0,1), what is the asymptotic distribution of b?
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct? a. When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. b....
Consider the simple linear regression model: HARD1 = β0 + β1*SCORE + є, where є ~ N(0, σ). Note: HARD1 is the Rockwell hardness of 1% copper alloys and SCORE is the abrasion loss score. Assume all regression model assumptions hold. The following incomplete output was obtained from Excel. Consider also that the mean of x is 81.467 and SXX is 81.733. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.450969 Standard Error Observations 15 ANOVA df...