Example 17-11. (a) Show that if a most efficient estimator A and a less efficient estimator B with efficiency e B-A tends to zero correlation with A. tend to joint normality for large samples, (b) Show that the error in B may be regarded as composed (for large samples) of two parts which are independent, the error in A and the error in (B –A). (c) Show further that V(A – B) = (! -1)V(A).
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML?ch 11. 4 Oxnard Petro, Ltd., has three interdisciplinary project development teams that function on an ongoing basis. Team members rotate from time to time. Every 4 months (three times a year) each department head rates the performance of each project team (using a 0 to 100 scale, where 100 is the best rating). Are the main effects significant? Is there an interaction?
- Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML? For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.Suppose that index model for Stocks A and B is estimated from excess returns with the following results : Ra 0.04 +0.6Rm+ea , Rb = - 0.04 + 1.3Rm + eb Risk on the market is 30% , R-squared of A is 30%R - squared of B is 40% , security A residual variance isA possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5-9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.31 What are the appropriate null and alternative hypotheses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hypotheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the criticalvalue method. *8.34 Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke. *8.35 Assuming this is regarded as a pilot study, how many…
- Note- bolded quiz have already answered A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5-9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.31 What are the appropriate null and alternative hypotheses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hypotheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the criticalvalue method. *8.34 Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke. *8.35 Assuming…If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value. B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.Which of the following is NOT a good reason for including a disturbance term in a regression equation? Select one: a. It captures omitted determinants of the dependent variable b. To allow for errors in the measurement of the dependent variable c. To allow for random influences on the dependent variable d. To allow for the non-zero mean of the dependent variable
- QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesisFor some genetic mutations, it is thought that the frequency of the mutant gene in men increases linearly with age. If m1 is the frequency at age t1, and m2 is the frequency at age t2, then the yearly rate of increase is estimated by r = (m2 − m1)/(t2 − t1). In a polymerase chain reaction assay, the frequency in 20-year-old men was estimated to be 17.7 ± 1.7 per μgDNA, and the frequency in 40-year-old men was estimated to be 35.9 ± 5.8 per μg DNA. Assume that age is measured with negligible uncertainty.a) Estimate the yearly rate of increase, and find the uncertainty in the estimate.b) Find the relative uncertainty in the estimated rate of increase.Question 2: Assume that the risk-free rate, RF, is currently 8%, the market return, RM, is 12%, and asset A has a beta, of 1.10. (could be done on word document or excel). Assume that as a result of recent events, investors have become more risk averse, causing the market return to rise by 2%, to be14%. Ignoring the shift in part c, draw the new SML on the same set of axes that you used before, and calculate and show the new required return for asset A. From the previous changes, what conclusions can be drawn about the impact of (1) decreased inflationary expectations and (2) increased risk aversion on the required returns of risky assets?