In linear models the Variance-Covariance matrix plays key role when estimating the parameters.State the variance-covariance structure of Population-averaged models: ( generalized estimatingequations-GEE) for B and Subject-specific models: Likelihood methods based on yi - MVN (Xy,V)to estimate y and parameters in V,Show that for OLS Y = X'B + ɛ the estimator B can be derived to B = (X'X)¯'x'Y with%3DVar(ß) = (X'X)-'o?

In linear models, the variance-covariance matrix plays a key role when estimating the parameters.…

Answered: In linear models the…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
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…
Linear Regression models can be optimised to avoid high variance by means of regularisations such as Lasso and Ridge. Explain when and why they are applied and the difference between both.
Consider multiple regression in matrix setting. LSE estimators beta hat=(X'X)^-1X'Y,with mean od beta and covariance of sigma^2(X'X)^-1. Why the residual vector is uncorrelated with the LSE estimators?
Prove that the slope of the sample regression function (B2) is the blur of the assumption s of gauss Marko theorem are satisfied make sure to show all the steps and the underlying assumptions
Two different plasma etchers in a semiconductor factory have the same mean etch rate μ. However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that the variance of etch rate for machine 1 is σ12, and for machine 2, it is σ2 = σ 2 12 a . Suppose that we have n1 independent observations on etch rate from machine 1 and n2independent observations on etch rate from machine 2.(a) Show that ˆμ = +− α α X X ( ) 1 2 1 is an unbiased estimator of μ for any value of α between zero and one.(b) Find the standard error of the point estimate of μ in part (a).(c) What value of α would minimize the standard error of the point estimate of μ?(d) Suppose that a = 4 and n n 1 2 = 2 . What value of α would you select to minimize the standard error of the point estimate of μ? How “bad” would it be to arbitrarily choose α= . 0 5 in this case?
If in a multivariate regression model with significant F-value, all the estimated parameters have computed-t values less than 1, then the model is likely to have _____. Select one: a. partial correlation for each regressor is insignificant b. some or all the regressors are linearly dependent c. a problem of multicollinearity d. all of the above
If X is a random variable with expectation µ and variance cµ2 , where c is a constant. Find a variance stabilizing transformation of X.
3- Heteroskedasticity refers to the residuals from a regression model Select one:Being linearBeing independentHaving a constant varianceHaving time-dependent varianceClear my choice
An analyst believes that the only important determinant of banks’ returns on assets (Y) is the ratio of loans to deposits (X). For a random sample of 20 banks, the sample regression line y = 0.97 + 0.47x was obtained with coefficient of determination 0.720. a. Find the sample correlation between returns on assets and the ratio of loans to deposits. b. Test against a two-sided alternative at the 5% significance level the null hypothesis of no linear association between the returns and the ratio.
Q#3. How can we detect Multicolinearity?. Write down the criterion of VIF, TOL and correlation matrix.
Consider a simple regression Y = B1 + B2 X + u. Suppose we found out that the variance of error term is changing with larger values of X (heteroscedasticity). Show how you overcome the problem of heteroscedasticity by using White’s heteroscedasticity consistent variances (only for variance of the slope estimate). Show and explain.

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