Using the file "happiness.csv" from a hypothetical study on quality of life as a measure of happiness, which asked how happy are you? With answers ("not", "pretty", "very")-happy. The study also collected income, recorded sex of respondent and if they believed in "heaven" (as a measure of spirituality). A researcher would like to study whether income may affect males and females differently and consider the "heaven" variable as a confounder. He wants to use an ordinal logistic regression model for this study. Please answer the following questions. (12 points)

• 3.2 If the following is the model output from the ordinal logistic regression model, please answer:

## Call: ## polr(formula = happy ~ heaven + sex * income, data = happyl) ##  ## Coefficients: ## Value Std. Error t value ## heavenyes -0.2009 0.1637 -1.2277 ## sexmale 1.4180 0.1423 9.9621 ## incomelow 0.1625 0.1839 0.8839 ## sexmale:incomelow -3.8938 0.3035 -12.8289 ##  ## Intercepts: ## Value Std. Error t value  ## not|pretty -1.5645 0.1874 -8.3506 ## pretty|very 1.9715 0.1952 10.1007 ##  ## Residual Deviance: 2213.388  ## AIC: 2225.388 

• What is the cumulative odds of a response of at least "not happy" among the individuals withheaven= no,sex= female, andincome= high? (1 point)
• What is the cumulative odds of a response of at least "pretty happy" among the individuals withheaven= no,sex= female, andincome= high? (1 point)
• For those who believe in heaven and have high income, what is the odds ratio of a happier response by males vs females? (1 point)
• For those who believe in heaven, what is the odds ratio of a happier response by males with low income vs.females with high income? (1 point)
• Is the interaction term significant? Should he drop the interaction term from the model? (1 point) Hint: You need to present the p-value.
• Is theheavenvariable significant? (1 point) Hint: You need to present the p-value.
• Isheavena confounder? Please use codes and output to explain.