11- what will you conclude about a regression model if the Breusch-Pagan test results in a p-value www smaller than the level of significance? Please select one; a) this implies no evidence of serial correlation b) this implies no evidence of heteroskedasticity c) this implies evidence of heteroskedasticity d) this implies evidence of serial correlation
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- Discuss the FIVE (5) importance of adding error term in the regression model.C. "If two series are cointegrated, it is not possible to make inferences regarding the cointegrating relationship using the Engle-Granger technique since the residuals from the cointegrating regression are likely to be autocorrelated." How does Johansen circumvent this problem to test hypotheses about the cointegrating relationship? D. Compare the Johansen maximal eigenvalue test with the test based on the trace statistic. State clearly the null and alternative hypotheses in each case.Introductory Econometris: A Modern Approach 4th edition, Chapter 17 Problem 1CE: What is the command in R in order to run the "White heteroskedasticity-consistent standard errors & covariance"? In other words, I would like to run the new regression with robust standard errors in it.
- 1.5 Version B. Consider a panel data regression model Yit = Bo + B1 Xit + a; + eit where the unobserved heterogeneity a; is a fixed effect, and the idiosyncratic error eit is white noise. Is the random effect estimator of B1 consistent? Explain briefly.Consider the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied whena) Zi is independent of (Yi, Xi, Wi)?b) Zi=Wi?c) Wi is1 for all i?d) Zi=Xi?1.5 Version B. Consider a panel data regression model Yit = Bo + B1Xit + a; + eit where the unobserved heterogeneity a; is a fixed effect, and the idiosyncratic error et is white noise. Is the random effect estimator of B1 consistent? Explain briefly.
- 10. Residual analysis Consider a regression of y on several independent variables, and the resulting predicted values of the dependent variable. The residual for the ith observation Consider a data set for a large sample of professional basketball players. Each observation contains the salary, as well as various performance statistics such as points, rebounds, and assists for each player. Suppose a regression of salary on all performance statistics is run, and the residuals are obtained. The player with the lowest (most negative) resid represents which of the following? (Assume the regression reasonably predicts salaries in most cases.) The most fairly paid player relative to her on-court performance The most overpaid player relative to her on-court performance The highest-paid player, regardless of her on-court performance The most underpaid player relative to her on-court performance2. Consider a two variable regression model, which satisfies all the Gauss Markov assumptions except that the error variance is proportional to X² i.e.E(u?) = o²X? Y₁ = B₁ + B₂X₁ + Ui How would you obtain the best linear unbiased estimates from the above regression.1. Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids = 0 + 1educ + u, where u is the unobserved error. (a) What kinds of factors are contained in u? Are these likely to be correlated with level of education? (b) Will a simple regression analysis uncover the ceteris paribus eect of education on fertility? Explain.
- 1. When considering a Simple Linear Regression model, a. Describe a test that is performed to decide whether there is a statistically significant linear relationship between the dependent an independent variables? b. What are the hypotheses for the test? c. What assumptions does the test make? d. What is the formula for the test statistic used in the test? e. What is the consequence of failing to reject the null hypothesis, Ho?1. You are interested the causal effect of X on Y, B1. Suppose that X, and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias due to the exclusion of X2? (a) Yes (b) No (c) Maybe 2. Omitted variable bias violates which of the following assumptions: (a) The conditional distribution of u, given X1i X2i, ...Xki has a mean of zero (b) (Xi, X2i...Y;), i = 1, ., n are independently and identically distributed (c) Heteroskedasticity (d) Perfect multicollinearity(1) An econometrician suspects that the residuals of her model mightbe autocorrelated. Explain the steps involved in testing this theoryusing the Durbin–Watson (DW) test. (2) The econometrician follows your guidancein part (b) andcalculates a value for the Durbin–Watson statistic of 0.95. The regression has 60 quarterly observations and three explanatory variables (plus a constant term). Perform the test. What is your conclusion?