You have a regression: Ỷ =0.42 + 0.9 X − 1.37X2 +0.61X3 (0.24) (0.5) (0.34) N = 50, R² = 0.67 What is the test statistic for Ho: B2 B3 B4 = 0 v.s. H₁: at least one of them is not zero 28.71 31.13 31.8 46.7
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- b. A regression on the original regressors, q₁² and a constant term yields the following statistics: R2 0.296041 F = 1.177507 coeff of q² has a t-statistic of 2.876 (i) With this information, which test can you implement to deal with the problem omitted variables and why? (ii) Implement the test as stated in b(i) and interpret the results. (iii) What is (are) the consequence(s) of the problem alluded to above on the estimators?Exercises 5.1 Suppose that a rescarcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression TestScore- 520.4 - 5.82 x CS, R² =0.08, SER = 11.5. (20.4) (2.21) a. Construct a 95% confidence interval for B, the regression slope coef- ficient. b. Calculate the p-value for the two-sided test of the null hypothesis Hs B1 -0. Do you reject the null hypothesis at the 5% level? At the 1% level?The covariance by itself is not very useful because ___________.
- (20.7) (1.35) Scenario 38-1. Consider the following OLS model applied to the data for workers wages and years of schooling, where e; stands for the residual: WAGE = -10.7+ 3.16 x SCHOOL + e. Refer to Scenario 38-1. Suppose that the residual term has a zero mean and is uncorrelated with the independent variable. Suppose that the standard error is 1.35. This means that we can be 95 percent confident that the true wage benefit of a year of schooling 000 is equal to $8. is equal to $0.46. lies between $0.46 and $5.86. lies between $8 and $13.4.Consider the following regression: Test Score, = 68.12 +2.52Hours Studied, - 0.04Hours Studied? %3D Without studying, an individual would average a test score ofA certain standardized test measures students' knowledge in English and math. The English and math scores for 10 randomly selected students were recorded and analyzed. The results are shown in the computer output. Predictor Coef SE Coef t-ratio Constant -124.13 78.712 0.046 Math 1.223 0.1966 6.220 0.000 S = 34.55 R-Sq = 82.8% R-Sq (Adj) = 83.5% Which of the following represents the standard deviation of the residuals? O 1.223 34.55 78.712 124.13
- You are given the estimated regression equation y=234-6.2X2+082X3 R-Square%-D0.42 (7.2) (0.95) (0.45) The number between parentheses are standard error the Sample size N=100 The test statistics to test that B2=-5 against the alternative that it is less than -5 is equal to O a. -6.526 O b. -1.263 C. -11.789 d. None of the option is correctIn column Es, I'm not sure how to get the results to show as .0583333 vs 58.33. I've included a copy of my formula. Thank you!When the regression error is heteroskedastic, all of the following statements are false, with the exception of: a. the conditional variance of the error term is not constant. b. the OLS estimator is unbiased but not consistent. C. the OLS estimator is still BLUE.
- You estimated a linear regression model with 3 explanatory variables using a sample of 29 observations. You are asked to test the overall significance of the model.the F-statistics calculated is equal to 2.567 and the F-critical at 5% level is 3.028. The p-value of the test can be expressed as: Select one: O a. P(F(3,25)<=2.567) O b. 1-P(F(3,25)<=2.567) O c. P(F(3,25)<3.028) O d. 1-P(F(3,25)<33.28)With Panel Data, if we assume that the individual effects vi are not correlated with the regressors Xit (i.e. E(vi|Xit) = 0), which one of the following statements is correct: The Fixed Effects estimator is not consistent. Both the OLS and the Random Effects estimators are not consistent. The OLS estimator is not consistent, but the Random Effects estimator is consistent. The OLS and the Random Effects estimator are consistent. All of the above. None of the aboveExplain Standard errors for TSLS (two stage least squares)?