The disturbance term in a regression model exhibits homoskedasticity if it has the same variance for all values of the independent variable. O True O False The correlation matrix is useless for revealing multicollinearity in a multiple regression problem because correlations are only pair-wise while multicollinearity involves more than two independent variables. O True False
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- Please no written by hand The assumption of normally distributed errors means that... A. errors can be ignored when doing regression modelling. B. the OLS estimators can also be assumed to be normally distributed since they are a linear functions of the errors. C. the OLS estimators can also be assumed to be normally distributed since they are BLUE. D. the OLS estimators can also be assumed to be normally distributed since they are minimum variance. E. the regression model will not be subject to specification error.A) State whether the following statement(s) are true/false with justification i) If the model is linear in parameters, but there is non-linear relation between dependent and independent variables, OLS cannot be used. ii) OLS can be applied to estimate a multiple linear regression model, and each slope coefficient shows the full effect of an individual variable on the dependent variable iii) Both slope and intercept will change if dependent and independent variables are divided by factor k (=1000). B) In a left-tailed test where you reject Ho only in the lower tail, what is the p-value if Z = (-) 1.00?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?
- Distinguish between the R2 and the standard error of a regression. How doeach of these measures describe the fit of a regression?Explain what is meant by an error term. What assumptions do we makeabout an error term when estimating an ordinary least squares regression?2. Which of the following types of regressions will always have a binary outcome variable? (A) Probit (B) Difference-in-differences (C) Regression discontinuity (D) (A) and (B) will both have binary outcome variables
- In a multiple OLS regression. Does correlation between explanitory variables violate assumtion number 4 multicolliniearity? Or is it just for perfect colinearity?1.1 Which of the following is NOT a good reason for including a disturbance term in a regression equation?/ A. To allow for random influences on the dependent variable/ B. To allow for errors in the measurement of the dependent variable/ C. It captures omitted determinants of the dependent variable D. To allow for the non-zero mean of the dependent variable/ 1.2 Consider the equation Y = B1 + B2X2 + u. A null hypothesis of H0: B2 = 0 means that/ A. X2 has no effect on the expected value of Y / B. B2 has no effect on the expected value of Y/ C. X2 has no effect on the expected value of B2 / D. Y has no effect on the expected value of X2/ 1.3 The OLS residuals in the multiple regression model/ A. can be calculated by subtracting the fitted values from the actual values / B. are zero because the predicted values are another name for forecasted values / C. are typically the same as the population regression function errors / D. cannot be calculated because there…What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?
- If we run a regression where y (bankruptcy) = f (factors potentially predicting bankruptcy), what is the dependent variable?5 We are given a sample of n observations which satisfies the following regression model: yi = β0 + β1xi1 + β2xi2 + ui , for all i = 1, . . . , n. This model fulfills the Least-Squares assumptions plus homoskedasticity. (a) Explain how you would obtain the OLS estimator of the coefficients {β0, β1, β2} in this model. (You do not need to show a full proof. Writing down the relevant conditions and explain)Subject: Economics Let ei be the ith residual in the ordinary least squares regression of y on X in the classical regression modeland let εi be the corresponding true disturbance. Prove that plim(ei - εi) = 0