Consider the following regression model: Y₁ =B₁ + B₂X₂1+ B3X31+ B₂X41 +24₁ Using the model above show that the maximum likelihood estimator for the variance, var (uX21-X31-B4X4), is biased (be sure to comment of the nature of the bias).
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- Can logistic regression be used in both prospective and retrospective study? Will the odds ratios of the effect of the predictor on the response are different under these two study designs? What formula can we use to solve maximum likelihood estimate of regression coefficient beta in Poisson regression (with log link)? can ridge regression be applied if sample size is smaller than the number of predictors? if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?In a multiple linear regression model with 3 predictor variables, what is the t-statistic for the hypothesis test of the null hypothesis that the coefficient of the second predictor variable is equal to 0, if the estimated coefficient is 0.5, the standard error of the estimate is 0.1, and the degrees of freedom is 15?State the large-sample distribution of the instrumental variables estimator for the simple linear regression model, and how it can be used for the construction of interval estimates and hypothesis tests.
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