Suppose we fit a Poisson regression model with log link to a dataset whose response variable is a count. No offset is included. In the fitted model we have included a covariate x. and the estimated coefficient of x is b. Suppose that we then decide to fit the same model. but with it included as an offset as well as included in the linear predictor as before. Which of the following statements is correct? Notes: {i} Precisely one answer below is correct and the others are incorrect. {iii An incorrect answer scores zero while the correct answer scores full marks for the question. Select one: a. b decreases by l and the deviance will not change. b. b increases by i and the deviance will not change. b decreases by l and the deviance will {usually} change. D D D D ['1 d. b increases by i and the deviance will {usually} change