Q. 6 What are the Gauss–Markov conditions that should hold for estimator to be BLUE ? Differentiate between Hetroskedasticty and multi-collinearity?
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Q. 6 What are the Gauss–Markov conditions that should hold for estimator to be BLUE ?
Differentiate between Hetroskedasticty and multi-collinearity?
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- A research center claims that at least 28% of adults in a certain country think that their taxes will be audited. In a random sample of1000 adults in that country in a recent year, 23%say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. nothing% of adults in the country think that their taxes will be audited. B. Less than nothing% of adults in the country think that their taxes will be audited. C. At least nothing% of adults in the country think that their taxes will be audited. D. The percentage of adults in the country who think that their taxes will be audited is not nothing%. Let p be the population proportion of…Consider the fitted values from a simple linear regression model with intercept: yˆ = 7 + 4x. Assume that the total number of observations is n = 20. In addition, the explained sum of squares is SSE = 10 and the residual sum of squares is SSR = 30. Under the classical Gauss-Markov assumptions, a) What is the value of the R2 ?In the simple linear regression model , the Gauss Markov ( classical ) assumptions guarantee that the OLS estimator of the unknown parameters is BLUE. Among those assumptions , in order to have consistency of the OLS estimator we need ( this is a question on the necessary condition ): Question 4Select one: a. we need that the errors are not correlated with each others and that they have zero mean b. we need that the errors are homoscedastic ( all have the same variance) c. we need that the residuals are not correlated with the explanatory variables and that the residuals have zero mean d. we need that the errors have zero mean and that they are not correlated with the regressors ( no endogeneity) e. we need that the errors are homoscedastic ( all have the same variance) and not correlated with each others ( no serial correlation)
- a) What is the equation for this model? b) What are the null and alternative hypotheses? c) What is the level of significance? d) What is the test statistic and the p-value?1.ln a simple model Y = Bo + B1X +u, X is endogenous, and Z is an instrumental variable that satisfy the relevance and exogeneity conditions. Show that the two stage least squares (TSLS) estimator is consistent. 2.In above model, what is the asymptotic distribution of TSLS? How can we do a). hypothesis testing of Bi and b). construct confidence interval for B,?A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage of adults in the country who think that their taxes will be audited is not enter your response here%. B. enter your response here% of adults in the country think that their taxes will be audited. C. Less than enter your response here% of adults in the country think that their taxes will be audited. D. At least enter your response here% of adults in the country think…
- a production line is producing light bulbs. 90% of the bulbs are good and .10% are defective. Suppose each bulbls condition is dependent of the other bulbs condition Select three buls at randon: 1. P(all 3 are good)=? 2. P( 2 of 3 are good)= 3. P(1 of 3 are good)=In running a regression model with heteroscedastic errors, the estimators given by Weighted Least Squares (WLS) are BLUE. However, we should still use OLS method with heteroskedasticity-robust standard errors because a) this remedial method is simpler. b) the Gauss-Markov theorem holds. c) the exact form of the conditional variance is rarely known in practice. d) many econometric softwares do not have a command for weighted least squares.Example 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 8 8. 10 4 7 Marks in 2nd Test (Y) 8 7 7. 10 5 8. 10 6. (a) Find the least square regression line of Y on X. / 7,
- 1. Derive the least squares estimators (LSES) of the parameters in the simple linear regression model. 2. Derive the estimators of 30 and ß1 using maximum likelihood estimation procedures.Foofy obtained a significant Fobt from an experiment with five levels. She therefore concludes that changing every condition of the independent variable results in a significant change in the dependent variable. (a) Is she correct? Why or why not? (b) What must she now do?9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).
