Sample Questions
Question 1
Easy
In a GLM, Pearson residuals are defined as:
Solution
D is correct.
The Pearson residual for observation in a GLM is defined as:
where is the variance function of the assumed distribution evaluated at the fitted mean. This standardizes the raw residual by the expected standard deviation under the model.
The Pearson residual for observation in a GLM is defined as:
where is the variance function of the assumed distribution evaluated at the fitted mean. This standardizes the raw residual by the expected standard deviation under the model.
Question 2
Medium
In a GLM, the systematic component specifies:
Solution
C is correct.
The systematic component of a GLM specifies the linear predictor, which is a linear combination of the predictors: . This determines how the covariates enter the model.
The systematic component of a GLM specifies the linear predictor, which is a linear combination of the predictors: . This determines how the covariates enter the model.
Question 3
Hard
In OLS regression, which of the following conditions ensures that the coefficient estimates are unbiased?
Solution
E is correct.
For OLS estimates to be unbiased, two conditions are essential: (1) the model must be correctly specified (the true relationship is linear in the parameters included), and (2) the errors have zero conditional mean, . This ensures . Unbiasedness does not require normality, homoscedasticity, or uncorrelated predictors.
For OLS estimates to be unbiased, two conditions are essential: (1) the model must be correctly specified (the true relationship is linear in the parameters included), and (2) the errors have zero conditional mean, . This ensures . Unbiasedness does not require normality, homoscedasticity, or uncorrelated predictors.
