State hypotheses test statistic and df p-value
Refer to Exercise 26 from Chapter 4 on the Alcohol Consumption data, in which a Poisson regression model was fit using first Saturday drink consumption as the response and prel, nrel, posother, negother, age, rosn, and state as the explanatory variables. Examine the fit of this model and draw conclusions.
Exercise 26
Consider an expanded regression model for the alcohol consumption study from Section 4.2. We will use a model that regresses the number of drinks consumed (numall) against positive romantic-relationship events (prel), negative romantic-relationship events (nrel), age (age), trait (long-term) self-esteem (rosn), state (short-term) self-esteem (state), and two other variables that we will create below. We will again use Saturday data only.
The negevent variable is the average of the ratings across 10 different types of “life events,” one of which is romantic relationships. We want to isolate the relationship events from other events, so create a new variable, negother, as 10*negevent – nrel. Do the same with positive events to create the variable posother.
(a) Construct plots of the number of drinks consumed against the explanatory variables prel, nrel, posother, negother, age, rosn, and state. Comment on the results: which variables seem to have any relationship with the response?
(b) Fit the full model with each of the variables in a linear form. Report the regression parameter estimates, standard errors, and confidence intervals. Do these estimates make sense, considering the plots from part (a)?
(c) Conduct LRTs on the regression parameters to determine which corresponding variables make a significant contribution to the model. State the hypotheses, test statistic, p-value, and use the results to draw conclusions regarding the contributions of each variable to the model.
(d) Determine whether any variables except the two negative events variables are needed in the model. To do this, refit the model with only nrel and negother. Perform a LRT comparing the full model above with this reduced model. State the hypotheses, test statistic and df, p-value, and conclusions.
