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- 1) Assuming you have a data matrix X that has n rows and p variables and you know both µ and Σ. How is (X- µ)‘Σ-1(X- µ) distributed? 2) Assuming that you don’t know the values of µ and Σ. How is the statistical distance distributed as n-p gets large?By hand, compute the correlation matrix R that goes with the covariance matrixExplain Homoskedasticity-Only Standard Errors of the covariance matrix?
- Given that the σ_AB= σ_BA, then the variance-covariance matrix for a portfolio with 50 stocks requires the calculations of ____ variances and ____ covariances.For a system of 3 equations using FGLS where I imposed a restriction on omega_hat that the residuals, u1 and u2 are uncorrelated, but u1 and u3 are correlated. How do you estimate/code omega in SAS using FGLS given the conditions above?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…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. Suppose 40 children, both of whose parents smoke, and50 children, neither of whose parents smoke, are recruitedfor the study.*8.37 How much power would such a study have using atwo-sided test with significance level = .05, assuming thatthe estimates of the population parameters in the pilot studyare correct?*8.38 Answer Problem 8.37 assuming a one-sided ratherthan a two-sided test is used.
- If the non-zero singular values of the column centered matrix X element of R101x9 (number of features = 9) are 6,5,4,3,2,1. 1. Find the total variance explained by the first four principal components. 2. Find the spectral norm of the pseduo-inverse of X.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?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?
