1. When considering a Simple Linear Regression model, 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?
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- Consider 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=1Which of the following is true of heteroskedasticity? a) The R-squared statistic is affected by the presence of heteroskedasticity b) Heteroskedasticty causes inconsistency in the Ordinary Least Squares estimators c) The OLS estimators are not the best linear unbiased estimators if heteroskedasticity is present d) It is not possible to obtain F statistics that are robust to heteroskedasticity of an unknown formb. The following model is a simplified version of the multiple regression model used by BEST Econometrics Group to study the trade off between time spent sleeping and working to look at other factors affecting sleep: sleep Bo + B₁totwrk + B₂educ + Page + μ₁ where sleep and totwork (total work) are measure in minutes per week and educ and age are measured in years. (i) If adults trade sleep for work, what is the sign of B₁? (ii) What signs do you think ₂ and 3 will have? (iii) Using the data in SLEEP75.RAW, the estimated equation is sleep = 3,638.25-.148totwrk-11.13educ - 2.20age, n = 706, R² = .113 If someone works five hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff? (iv) Discuss the sign and magnitude of the estimated coefficient on educ (v) Would you say totwrk, educ, and age explain much of the variation in sleep? (vi) What other factors might affect the time spent sleeping? (vii) Are these likely to be correlated with totwrk?
- Suppose we are interested in evaluating the impact on wages of being a college graduate and of residing in California. To this end we define the following dummy variables if college graduate if not college graduate coll = ncoll = if not college graduate if college graduate 1 cali = if residing in California S 1 if not residing in California ncali = if not residing in California if residing in California and for wages denoting yearly wages, we estimate the following model of returns to education wages = B1 coll+ B2ncoll + B3 cali + B4(coll x cali) + e where E[e|coll, cali] = 0. Which parameter or combination of parameters measures the increase in expected wages from obtaining a college degree (comparing to not having a college degree) when residing California? O a. None of the other options is correct O b. Bi – B2 O c. B1 – B2 + ß4 O d. B4 O e. Bi + B3 – ßi – B4 O f. Bi + B4 – ß2 – B4 Clear my choiceEconometrics Thomas Eisensee and David Stromberg wanted to measure how much news coverage of a foreign disaster impacted the amount of disaster relief provided by the U.S. government. They argue that the simple relationship would be biased. Let X = Minutes of News Coverage and Y= Disaster Aid. Choose a variable X2 that could bias the simple relationship. This variable should impact the amount of coverage and impact the amount of aid for reasons other than purely news coverage. Eisensee and Stromberg introduce an instrument Z = During the Olympics. Explain how Z could satisfy the relevant and exogenous criteria. Explain how you could use Z to estimate the impact of X on Y free from X2 bias. Hint: you should mention two stages.a. How to derive the variance and estimates of ols, and which steps in the derivation process require assumptions, list them.b. Under the classic OLS model. Given the R∧2 as well as the adjusted R∧2, discuss this two R-squared differences, advantages and disadvantages and their different roles.
- QUESTION 7 Which is NOT true about the coefficient of determination? As you add more variables, the R-square generally rises. As you add more variables, the adjusted R-square can fall. If the R-square is above 50%, the regression is considered significant. The R-square gives the percent of the variation in the dependent variable that is explained by the independent variables. The higher is the R-square, the better is the fit.19. The White test test statistic is n*R² ~x²(S-1). Where is the R² in the test statistic measured? A. The original econometric model when estimated using the White Robust Estimator B. The average from all the auxiliary regressions estimated with each explanatory variable as a function of the other explanatory variables C. The original econometric model before any test of heteroskedasticity has been performed D. The auxiliary regression of residuals as a function of the explanatory variables generating the heteroscedasticity 20. With annual times series data of 50 observations, how many observations are available to estimate the consumption econometric model CONt = Bo+ ß₁DISPYt + B₂CONt-1+ut A. 50 B. 47 C. 45 D. 49 21. Suppose the estimated simple linear demand equation for single-game tickets for a major football league is q=4.58-0.51p where q is the number of tickets sold measured in thousands and p is the dollar price of a ticket. Further assume that the point of the means_is…3. Boyoung is writing a paper about the effect of Sunday liquor sales on drunk driving. She has panel data on which states allow liquor to be sold on Sunday in which years and wishes to estimate a difference-in-differences model. She writes the following regression equation: Year DUIRate;; = atate +a? + BTreatmentt +yControl;t + Eit i Which of the following changes does Boyoung need to make? a) She should include a constant in the regression equation. b) She should not include controls because they're already accounted for by fixed effects. c) She should include a time trend instead of time-fixed effects. d) None of the above are changes she needs to make.
- 13. Collinearity in a multiple regression analysis Suppose you want to examine the effects of a training program on future earnings using the following model: earn98= 4.64 +2.376train +0.371earn96 +0.366educ- 1.86 age +2.534 married (1.14) (0.43) (0.016) (0.062) (0.013) (0.4) where earn 98- 1998 earnings, in thousands of dollars train -1 if the individual participated in the training program, and =0 otherwise earn 96- 1996 earnings, in thousands of dollars educ years of education age = age, in years married-1 if the individual is married, and -0 otherwise Suppose that there is a high degree of correlation (but not perfect) between earnings in 1996, education, age, and marital status. True or False: We should be concerned about this high degree of correlation because it affects our ability to reliably estimate the impact of the training program on 1998 earnings, T. True FalseQ. 30 The t test can be used for testing the JOINT significance of ALL explanatory variables x2, x3, and x4 in a multiple regression model. O True O FalseConsider a regression in which a coefficient suffers from downward omitted variable bias. If you add a regressor that controls for the omitted variable bias: Group of answer choices 1. Can’t determine 2. The new estimate will be smaller. 3. The new estimate will remain unchanged. 4. The new estimate will be larger