Given a 2-asset portfolio and two vectors of asset returns r and y, with volatility 15% and 30% respectively and correlation 0.70, determine the lincar combinations of a and y (principal components) that contribute to the overall variability of the portfolio.
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- Suppose you have obtained from SPSS the correlation matrix in Appendix 1. According to the information in this matrix, which two variables exhibit the strongest linear relationship?The relationship between the independent variable (IV) and the dependent variable (DV) is likely to be mediated by a third variable (MV). With regard to the statement above, which of the following is most likely to be correct? A IV = Students’ performance (i.e., marks) in the formative assessment; DV = Students’ performance (i.e., marks) in the summative assessment, and MV = Students’ level of comfort with the venue of the assessments B IV = Students’ performance (i.e., marks) in the summative assessment; DV = Students’ performance (i.e., marks) in the formative assessment, and MV = Students’ level of preparation for the assessments. C IV = Students’ performance (i.e., marks) in the formative assessment; DV = Students’ performance (i.e., marks) in the summative assessment, and MV = Students’ level of preparation for the assessments D IV = Students’ performance (i.e., marks) in the summative assessment; DV = Students’ performance (i.e., marks) in the formative assessment,…what does the equation, d/dt Π = MΠ calculate for where Π is population vector describing the overall state probability distributions and M is a 4x4 transition rate matrix?
- 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 this is regarded as a pilot study, how many…In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe, ros has no effect on CEO salary. State the alternative that better stock market performance increases a CEO’s salary.Which of the independent variables retains the strongest association with the number of children a respondent has when all other variables in the model are controlled?
- Is at least one of the two variables (weight and horsepower) significant in the model?Consider a cohort study to compare the mortality rate of myocardial infarction (MI) in men with sedentary work (exposed group) to men with physically active work (unexposed). If in the exposed, there were 36,000 person (man) years of observation and 126 deaths whereas the unexposed had 24,000 man-years of observation and 44 deaths. Compute the following a) Mortality rate in each cohort? b) What is the relative risk of dying, comparing these 2 groups? c) What is the attributable risk of sedentary work? d) What is the attributable benefit of physical activity? e) If we assume that MI is associated with the mortality in this cohort (causality), what proportion of the disease in the higher group is potentially preventable?If my hypothesis assumes that religious women are more satisfied with life than men, would gender be my dependent variable? Religion and satisfaction with life are both independent? Is that correct?
- 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. A) What are the appropriate null and alternative hypotheses to compare the means of the two groups? B) What is the appropriate test procedure for the hypotheses in Problem A? C) Carry out the test in Problem B using the criticalvalue method. D) 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.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 this is regarded as a pilot study, how many children…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. A) Assuming this is regarded as a pilot study, how many children are needed in each group (assuming equal numbers in each group) to have a 95% chance of detecting a significant difference using a two-sided test with α = .05? B) Answer the question in Problem A if the investigators use a one-sided rather than a two-sided test. Suppose 40 children, both of whose parents smoke, and 50 children, neither of whose parents smoke, are recruited for the study. C) How much power would…