Which of the following statements is/are TRUE? Select allthat apply.If the regression errors are homoskedastic, the OLS estimators areBLUE (best linear unbiased estimators) provided that the threeleast squares assumptions hold.Heteroskedastic errors violate at least one of the three leastsquares assumptions.The formulas to compute Standard Errors of the estimators areusually more simplified when you assume heteroskedastictiy.In the presence of heteroskedasticity, the OLS estimators are nolonger unbiased.If the errors are heteroskedastic but you assume that they werehomoskedastic, your computed standard errors will not be correct,and you won't be able to do valid statistical inference.

Homoscedasticity is the condition that the error term must have equal variance throughout he…

Answered: Which of the following statements…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please fill in the blanks with appropriate answers. - Of all possible estimators of α and β that are linear in the Yi and unbiased, the least squares estimators that have the smallest variances are said to be………………………….…………….……………………………. according to the…..………………………..……………… theorem. - The ……………………………………… is the proportion of the sample variability of the dependent variable explained by its linear relationship with the independent variable. Thanks.
Use the following linear regression equation to answer the questions. x1 = 1.9 + 4.0x2 – 7.5x3 + 2.4x4 (e) Suppose that n = 11 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.461. Construct a 99% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 10%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t t critical ± Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?Suppose x2 increased by 2 units. What would be the expected change in x1?Suppose x2 decreased by 4 units. What would be the expected change in x1?
a hypothesis test produces a t statistic of t=2.3. if the researcher is using a two tailed test with a=0.05 how large does the sample have to bw in order to reject the null hypothesis?
Which of the following is true of fixed effect estimators A. The fixed effects estimator is equal to the instrumental variable estimator if R^2 is equal to 1. B. The fixed effects estimators are biased if the regression model exhibits multicollinearity. C. The fixed effects estimators have lower variance than the ordinary least squares estimators. D. The fixed effects estimators have large standard errors when R^2 lies close to 0.
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a variance of 0.0025 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0 : ? H1 : ?
Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Suppose that n = 8 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.356. Construct a 95% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit _____ upper limit _____ b) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t = ____ critical t = _____
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0036. The actuaries of the company claim that the variance of thenumber of accidents per day is no longer equal to 0.0036. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.
A manufacturer of car batteries claims that the batteries will last, onaverage, 3 years with a variance of 1 year. Seven of these batteries havelifetimes, in years, as follows1.9, 2.4, 3.0, 3.5, 4.2, 5.1, and 11.24Construct a 99% confidence interval for σ2 . Assume the population ofbattery lives to be approximately normally distributed. Solve with proper solution
A hypothesis test produces a t statistic of t=2.01.If the researcher is using a two tailed test with x=0.05,how large does the sample have to be in order to reject the null hypothesis?
Suppose that you work for a company that manufactures parts for use in the aerospace industry where the dimensions of parts must be extremely close to their designed specifications (so very little variation). If the length of a particular part may be used as long as the maximum variance is 0.0004, which of the following pairs of hypotheses would you recommend for the appropriate hypothesis test in this case? A. H subscript O colon space sigma less or equal than 0.0004H subscript A colon space sigma greater than 0.0004 B. H subscript O colon space sigma greater or equal than 0.0004H subscript A colon space sigma less than 0.0004 C. H subscript O colon space sigma equals 0.0004H subscript A colon space sigma not equal to 0.0004
Use the following linear regression equation to answer the questions. x3 = −17.3 + 4.1x1 + 9.6x4 − 1.6x7 a) Suppose that n = 10 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.882. Construct a 90% confidence interval for the coefficient of x4. (Round your answers to two decimal places.) lower limit = ______ upper limit = ______ b) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x4 is different from zero. (Round your answers to three decimal places.) t= ____ t critical= ______
1. What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter ?? 2. Use the one-parameter regular exponential family definition to find the functions, ℎ(?),?(?),?(?) and ?(?).

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