Consider a multiple regression model: Y = B1 + B2X + B3 W + B4Z+ u, where Y is a dependent variable, X, W, and Z, are regressors, and u is a disturbance term. Suppose X = 2W + Z. Then the following is true: O The model suffers from nonlinearity in parameters O None of the presented possible answers are correct. O The model suffers from the lack of degrees of freedom O The model suffers from perfect collinearity O The model suffers from autocorrelation
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- QUESTION 1 In the equation, y = 8o + Bjx1 + 8zx2 + u, 8z is a(n) O a. intercept parameter O b. slope parameter O. dependent variable O d. independent variable QUESTION 2 If an independent variable in a multiple linear regression model is an exact linear combination of other independent variables, the model suffers from the problem of O a. perfect collinearity O b.heteroskedasticty O . homoskedasticity O d. omitted variable bias QUESTION 3 Which of the following is true of R 2? O a. R- usually decreases with an increase in the number of independent variables in a regression. O b.R2 shows what percentage of the total variation in the dependent variable, Y, is explained by the explanatory variables. OC.A low R2 indicates that the Ordinary Least Squares line fits the data well. O d. R² is also called the standard error of regression. QUESTION 4 We estimate the model Wage, = -2.91+0.568educ; + 0.033 exper; +0.115 tenure; by OLS, where wage is the hourly wage of a worker measured in dollars,…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…If you included both time and entity fixed effects in the regression model which includes a constant, then: O a. you have perfect multicollinearity. O b. you can exclude the constant and one entity binary variable to estimate the model. you can exclude the constant and one time binary variable to estimate the model. O d. you can exclude one time binary variable and one entity binary variable to estimate the model. O e. All of the above. Of. None of the above.
- 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 multicollinearityWhich of the following statements about the R-squared statistic of a linear estimation (or linear regression) is true? An R-squared statistic of 0.6 means the variation of the independent (explanatory) variable explains about 60% of the variation of the dependent variable. O An R-squared statistic of 0.6 means 60% the variation of the dependent variable cannot be explained by the variation of the independent (explanatory) variable. O An R-squared statistic of 0.6 means the variation of the dependent variable explains about 60% of the variation of the independent (explanatory) variable.Yi = B1 + B2xi2 + · · · + Brxik + ei, i = 1, . .., N, var (e; X) = var (y:|X) = o? Which property of linear regression model is most appropriate for the above regression? Select one: O a. heteroskedasticity O b. strict exogeneity c. autocorrelation O d. model mis-specification
- 2. 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.The table to the right contains price-demand and total cost data for the production of projectors, where p is the wholesale price (in dollars) of a projector for an annual demand of x projectors and C is the total cost (in dollars) of producing x projectors. Answer the following questions (A) - (D). (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. X 270 360 520 780 The fixed costs are $. (Round to the nearest dollar as needed.) ITTI y = (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) Use the linear regression equation found in the previous step to estimate the fixed costs and variable costs per projector. The variable costs are $ per projector. (Round to the nearest dollar as needed.) (C) Find the break even points. The break even points are (Type ordered pairs. Use a comma to separate answers as needed. Round to the nearest integer as…The following graph of the estimated residuals from a regression against the observation date (i.e. time period) indicates the residuals are: 2.00 1.50 1.00 0.50 00 0.00 -0.50 -1.00 1.50 -2.00 Time Select one: O A. Serially correlated O B. Normally distributed OC. Homoscedastic O D. Serially uncorrelated O E. Heteroscedastic Estimated residuals
- d/My courses / Faculty Of Economics & Administratiive Sciences / ECON309 / Finals / ECON 309 Fin 13. In the simple linear regression model, the regression slope a. O a. indicates by how many percent Y increases, given a one percent increase in X. ut of O b. represents the elasticity of Y on X. uestion Oc. when multiplied with the explanatory variable will give you the predicted Y. O d. indicates by how many units Y increases, given a one unit increase in X. nage(2)What would the consequence be for a regression model if theerrors were not homoscedastic?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)