Consider a linear model with 178 observations, 6 regressors and a constant with a R2 is...
Consider the Bayesian linear regression model with K regressors where v) Now suppose that we have an uninformative prior such that Show that the posterior verifies: N/2 where VĮß-σ2 (XX)-1.
Consider the Bayesian linear regression model with K regressors where v) Now suppose that we have an uninformative prior such that Show that the posterior verifies: N/2 where VĮß-σ2 (XX)-1.
Bayesian regression Consider the Bayesian linear regression model with K regressors where (v) Now suppose that we have an uninformative prior such that Show that the posterior verifies 2a2 where VĮß-σ2 (XX)-1. (vi) Now suppose that there is only one regressor li (ie. K = 1). Show that o2 N2 vii) Comment on how the result in part (vi) relates to the choice of prior and standard frequentist (i.e. non-Bayesian) estimators.
Bayesian regression Consider the Bayesian linear regression model with...
Bayesian regression Consider the Bayesian linear regression model with K regressors where (v) Now suppose that we have an uninformative prior such that Show that the posterior verifies 2a2 where VĮß-σ2 (XX)-1. (vi) Now suppose that there is only one regressor li (ie. K = 1). Show that o2 N2 vii) Comment on how the result in part (vi) relates to the choice of prior and standard frequentist (i.e. non-Bayesian) estimators.
Bayesian regression Consider the Bayesian linear regression model with...
1. Consider a linear regression model of y on K regressors and an intercept. (i) Describe the Breusch-Pagan test of heteroskedasticity. (ii) What are the consequences for OLS estimation and testing of rejecting the null hypothesis of the BP test? (iii)What can you say about the form of Heteroskedasticity function implied by BP? What if it is wrong? (iv) Describe the test of heteroskedasticity proposed by White. (v) When there is only one regressor (K=1), give the expression for White’s...
(Round all intermediate calculations to at least 4 decimal places.) Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. Linear Quadratic Cubic Intercept 25.97 20.73 16.20 x 0.47 2.82 6.43 x2 NA −0.20 −0.92 x3 NA NA 0.04 R2 0.060 0.138 0.163 Adjusted R2 0.035 0.091 0.093 pictureClick here for the Excel Data File a. Predict y for x = 3 and 5 with each of the...
Two linear regression models are fitted using software and below is their R2 and adjusted R2 values. Which of the two models fits the data better? Why does it fit the model better? In order from Model, R specification, R2, Adjusted R2 Model Model 1 : Y ∼ X1 + X3, 0.91, 0.84 Model 2 : Y ∼ X1 + X2, 0.88, 0.86
1. Consider the following linear regression model: (a) Which assumptions are needed to make the B, unbiased estimators for the B, (b) Explain how one can test the hypothesis that A +As = 0 by means of a t-test. (c) Explain how one can test the hypothesis that A-A-0. Indicate the relevant test statistic. (d) Suppose that ri is an irrelevant explanatory variable in the population model and that you estimate the model including both and r2. What are the...
Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. Linear Quadratic Cubic Intercept 9.66 10.00 10.06 x 2.66 2.75 1.83 x2 NA −0.31 −0.33 x3 NA NA 0.26 R2 0.810 0.836 0.896 Adjusted R2 0.809 0.833 0.895 a. Predict y for x = 1 and 2 with each of the estimated models. (Round intermediate calculations and final answers to 2 decimal places.) b. Select the most appropriate...
Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. Intercept х x2 Linear 28.53 0.12 NA NA Quadratic 28.80 0.01 0.01 Cubic 28.62 0.15 -0.02 -0.01 x3 NA R2 Adjusted R2 0.005 -0.021 0.006 -0.048 0.006 -0.077 a. Predict y for x = 2 and 4 with each of the estimated models. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal...
5. Consider the observations on two responses, ri and r2, displayed in the form of the following two-way table (note that there is a single observation vector at each combination of factor levels): Factor 2 Level 1 Level 2 Level 3 Level4 Level 1 6 12 Factor 2 Level 2 (3 Level 3 3 with no replications (i.e. n = 1), the two-way MANOVA model is Zij = μ +Ti + β, +Ej, i=1,2, 3. j = 1.2.3.4.