Q1. The bivariate distribution of the random variables X and Y is shown in the following table.X=0X=1TotalY=0Y=1 0.40.2 0.10.3 0.50.5 Total 0.6 0.4 1.0 Compute the covariance between X and Y.00.090.100.30 Q2The bivariate distribution of the random variables X and Y is shown in the following table, whichis the same as in the previous question.X=0X=1TotalY=0Y=1 0.40.2 0.10.3 0.50.5 Total 0.6 0.4 1.0 Compute the conditional expectation of Y, given that X = 1.0.330.500.600.75 Q3Suppose that a large company knows the following statistics about its employees: 20% of the employees work at the headquarters.60% of the employees are married.Among the employees working at the headquarters, 75% are married.What percentage of the employees are married people working at the headquarters?5%15%35%45%Q4Suppose that a large company knows the following statistics about its employees: 20% of the employees work at the headquarters.60% of the employees are married.Among the employees working at the headquarters, 75% are married.These are the same statistics as in the previous question. Among all married employees, whatpercentage work at the headquarters?12.5%20%22.5%25%Q5Consider the following bivariate distribution:Y=0 Y=1 Y=2 Total X=0X=1 0.16 0.16 0.080.30 0.12 0.18 0.400.60 Total 0.46 0.28 0.26 1.00 Are X and Y independent? Yes.No, because they have a bivariate distribution.No, because their correlation is not zero.No, for a different reason than those stated in the other answers. Q6Which of the following combinations is not possible?The correlation between X and Y is zero, and X and Y are independent.The correlation between X and Y is zero, and X and Y are dependent.The correlation between X and Y is nonzero, and X and Y are independent.The correlation between X and Y is nonzero, and X and Y are dependent. Q7Suppose that the following model was estimated using least squares regression:where a person’s life expectancy and education are both measured in years. We find the estimate. What does this mean?A person who stays in school for one additional year can be expected to live 0.15 yearslonger.A person who stays in school for one additional year can be expected to live for a 15% longertime.A person with an average level of education can be expected to live 0.15 years longer than aperson with the legal minimum level of education.A person with an average level of education can be expected to live 15% longer than aperson with the legal minimum level of education.Q8We have a sample with means, what is the value of2 andthat is found? . If least squares regression of y on x results in 38Not enough informationQ9When performing linear regression, which of the following is a residual? a. a.b.c.d. Q10If least squares regression results in , what can we say about ? b.c.d.Q11In the model , we find the estimate with standard error 0.4, based on a sample with 25 observations. Compute a 95% confidence interval forrelevant critical value can be found in the following table.22 23 24 25 26 27 2.074 2.069 2.064 2.060 2.056 2.052( -0.228, 1.428 )( -0.224, 1.424 )( 0.434, 0.766 )( 0.435, 0.765 ) . The Q12Which of the following will cause the standard error ofA lower intercept. to go down? A smaller sample size.More variance in the error term.More variance in the regressor. Q13What is heteroskedasticity? a. All of the have the same variance. b. All of the can have different variances. c. All of the have the same variance. d. All of the can have different variances. Q14Two of the assumptions that we generally make when performing least squares regression are:•• for all i;for all i.Which of these assumptions is/are necessary to prove unbiasedness of the least squaresestimators?The first one is necessary, but the second one is not.The first one is not necessary, but the second one is.Both are necessary.Neither are necessary. Q15What does the Gauss-Markov theorem say about estimators ofthan the least squares estimator that have a smaller variance ? They cannot exist.They may exist, but they must be biased or non-normally distributed.They may exist, but they must be biased or nonlinear.They may exist, but they must be non-normally distributed or nonlinear.Q16What is true about the least squares estimator ? a. It is not a random variable, because we have an exact formula for computing it.b. It is a random variable because it is a population quantity, so we don’t know its exact value.c. It is a random variable because it depends on our choice to minimize instead of, for example,. A different choice would give a different result.d. It is a random variable because it depends on the particular data that we analyze. A different sample would give a different result. Q17In the linear regression model, we sometimes assume that the disturbance termnormal distribution. Does this imply that the estimator follows a also follows a normal distribution? a. Yes, it does.b. Only if follows a normal distribution too. c. Only if follows a normal distribution too. d. No, follows a t distribution. Q18Suppose that the standard two-sided t test for the null hypothesis0.47. What can you conclude? Q19 results in a p-value of a. There is enough evidence to say that . b. There is enough evidence to say that . c. There is not enough evidence to say that . d. There is not enough evidence to say that . After having estimated a regression modelof given a new observation conditional mean ofof these predictions? , we wish to forecast the value . We can consider two types of predictions: forecasting the , or forecasting the actual value of . What is true about the variances a.b. c.d.than may be larger or smaller , depending on the data set. Q20When working with the time series regression modelshould one use HAC standard errors? , in which case a. If we suspect that there is correlation between and . b. If we suspect that there is correlation between and . c. If we suspect that there is correlation betweend. Always, just to be on the safe side. and .
ECMT 1020 – The bivariate distribution of the random
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