In the ERtemp dataset on the class site, 200 days were sampled at 2 hospitals in Los Angeles. The number of emergency room (ER) admissions for blunt force trauma injuries and the outdoor high temperature was recorded for each day. Researchers wanted to quantify how much does temperature affect the number of events of ER ad- missions for accidents and injuries on a given day. The reasoning is that the higher the temperature, the more outdoor activities and traveling lead to higher ER admission for injuries. a. Each observation in this dataset was across the same period of time (24 hour). Does the model need an offset term? Write out the population model that will be estimated using correct notation. b. Fit a Poisson regression model where the response is the count of events over a day, and the explanatory variable is the daily high temperature (in Fahrenheit). Write the estimated model and interpret the effect of a unit increase in temperature on the count of events. Now interpret the effect of a 15 unit increase in temperature. C. Estimate the expected count of events when the temperature is 85 degrees. Create a 95% confidence interval for the true expected count when temperature is 85 degrees. Interpret this interval in context of the problem. d. Test if the coefficient on temperature is equal to 0 or not using a Z-test. Write the null and alternative. State the p-value and make a conclusion in context of the problem. e. Compare the null deviance to the residual deviance. Is there a big difference? How does this information relate to the test you conducted in part d.?