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.
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- If the error term covariance matrix is not spherical, but it is diagonal, then you have: Autocorrelation, but no heteroskedasticity. Heterskedasticity and autocorrelation. Heteroskedasticity, but no autocorrelation. Both heteroskedasticity and autocorrelation. Neither hetroskedasticity or autocorrelation.Y 70 12 50 9 57 60 14 43 9 52 11 i. Find the estimators for Bi and B2 correct to decimal points and fit the regression equation for X and Y when X is the explanatory variable. Interpret the results from the obtained equation. calculate the sum of error squared. Find the variance of the sum square error ii. iii. iv. Find the standard error for B2 Find the coefficient of correlation and give its interpretation V. vi.Describe the important characteristics of the variance of a conditional distribution of an error term in a linear regression. What are the implicationsfor OLS estimation?
- The variance of the OLS estimator Select one: a. increases as the number of observations increases b. increases as the variance of the unobservable increases c. decreases as the number of observations increases d. decreases as the variance of the unobservable increases e. c) and d) are true f. b) and c) are true g. a) and b) are trueConsider the output here from a regression in R. What is 3₂? Coefficients: Estimate (Intercept) 1.708 5.404 -1.478 9.531 X1 X2 X3 Std. Error 0.555 2.792 0.6 2.758Define the Ordinary Least Square estimator is linear and conditionally unbiased?
- The dependent variable is used to predict the independent variable. Is this True or False1) In the method,two independent variable are assumed to have; a)Low collinearity b)High collinearity c)No collinearity d)Perfect collinearity 2) If variance of coefficient cannot be applied, we cannot conduct test for; a) Correlation b) Determination c)Significant d) Residual termThe regression equation Netincome = 2,049 +.0478 Revenue was estimated from a sample of 100 leading world companies (variables are in millions of dollars). (0-1) If Revenue = 1, then Netincome = (a-2) Choose the correct statement. (b) Choose the right option. (c) O Increasing the revenue raises the net income. Decreasing the revenue raises the net income. O Increasing the revenue lowers the net income. million. (Round your answer to 2 decimal places.) O The intercept is not meaningful because a firm cannot have net income when revenue is zero. The intercept is meaningful because a firm can have net income when revenue is zero. If Revenue = 24,574, then NetIncome = million. (Round your answer to the nearest whole number.)
- In your own words, describe what the difference is between an error term and a residual. How does sample size affect the variance of each?Consider the OLS estimator 3;. Under the Gauss-Markov assumptions, O the estimator is the best linear unbiased estimator. O the estimator is asymptotically normally distributed. O the estimator has the properties stated in the other three possible answers. O the estimator is consistent.Given the following regression output, Predictor Coefficient SE Coefficient t p-value Constant 84.998 1.863 45.62 0.000 x1 2.391 1.200 1.99 0.051 x2 -0.409 0.172 -2.38 0.021 Analysis of Variance Source DF SS MS F p-value Regression 2 77.907 38.954 4.138 0.021 Residual Error 62 583.693 9.414 Total 64 661.600 answer the following questions: d-1. State the decision rule for 0.05 significance level: H0: β1 = β2 = 0; H1: Not all β's are 0. (Round your answer to 2 decimal places.) d-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) d-3. What is the conclusion? Use the 0.05 significance level.