Let Yi = 1 if they = 0 if individual i in the survey states that they look for an airbnb/VRBO first, and Yi look for a traditional hotel room first. Let Xli = 1 if individual i is between the ages of 18-24 and Xli :0 otherwise. 1. A researcher uses a logistic regression model for these data, and obtains the output below when they use R to fit the model. Estimate (Intercept) Age18to24 .95 -.61 Std. Error 0.17 0.22 z value Pr(>1z) 5.58 -2.77 Null Deviance Residual Deviance 256.78 215.76 Part 2 Now a second variable is added to the data. Let Xzi be the number of nights, on average, an individual spends in vacation housing during the year. Model 2 (Intercept) Agel8to24 Vacation Nights Estimate .95 -.46 .56 Std. Error 0.17 0.17 0.12 z value Pr(>[z) 5.58 -2.71 4.66 Model 2 Null Deviance Residual Deviance 256.78 199.98 Model 2 was built by Researcher A, who claims that we need to control for the number of nights a person stays in a hotel room before making any claims about the impact of age. 5. Build and interpret a 95% confidence interval for vacation nights in terms of the odds. Show your work. 6. What is the AIC for Model 1? 7. The Researcher wants to know if adding vacation nights into the model has improved model fit. They state that what they mean by "improving model fit is that Model 2 has an improved likelihood versus Model 1. Using a nested likelihood ratio test, provide an answer to the researcher's question? Show all your steps, and clearly state your answer in the context of the data. Hint: This means a sentence