Which of the following is a nonlinear regression model? O None of the presented possible answers are correct. O log Y = Bo + B1 log X+ u %3D OY = Bo + B1VX +u %3D OY = Bo + B1X + u O Y = PotB,X
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- .Please no written by hand solution a) Suppose in a regression of weekly salaries on years of schooling for males(m) and females(f), the following results are obtained. Wm = 50Sm and Wf = 40Sf. where Wm (Wf) denotes weekly salary and Sm (Sf) denotes years of schooling for males and females respectively. 50 and 40 are the coefficients on schooling in the male and female regression respectively. On average, men have 12 years of schooling and women have 10 years of schooling. What is the average male-female wage differential? Is this a good estimate of discrimination? Explain why/why not. Using the information in the question, what would you propose as a better estimate of discrimination? State any assumptions that you use and explain your answer.(2)What would the consequence be for a regression model if theerrors were not homoscedastic?
- 1What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?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
- 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 multicollinearityConsider the regression model Yi=bot Bi Xitui Suppose that you know Bo = 0. Derive the formula for the least squares estimator of B₁. The least squares objective function is O A. n O B. O C. O D. E (Yi-bo-b1Xi) i=1 n Σ (Yi-bo-biXi) i=1 2 n Σ (v₁²-bo-b₁x₁²) i=1 n E (Yi-bo-b+Xi) 3 i=1A scatter plot shows data for the cost of a vintage car from a dealership (y in dollars) in the year a years since 1990. The least squares regression line is given by y-25,000 + 500z. Interpret the y intercept of the least squares regression line. Select the correct answer below O The predicted cost of a vintage car from a dealership in the year is 820.000 O The predicted cost of a vintage car from a dealershpin the year 1090 is 85,000. O The predicted cost of a vintage car from a dealershp in the year 1990 is sse. The yintercept should not be interpreted.
- 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,…QUESTION 2 Continue to use the example from Question 1. Suppose each product is randomly assigned to a process by a computer program, but some products get reassigned on the factory floor (for practical reasons). Let Z¡ denote the original assignment and X¡ the actual process used to produce i. In a regression of Y¡ on X¡ and Wj, OLS is: d. Potentially biased because W; should not be included b. Potentially biased, but an IV regression using Z¡ as an instrument can be used to obtain a consistent estimator C. Unbiased because the products were randomly assigned in the beginning d. Unbiased as long as Zj is also included as a control variableEconometrics question