you deem an assumption to be violated describe what you might do to address this concern

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

The dataset “happiness.omv” contains 5 variables: STATE (Location in the United States), SOUTH (Whether the state is in the continental south, =1, or not =0), HAPPY (Average level of happiness in each state; standardized), SELF (Average level of positive self-esteem in each state; standardized) and SOCIAL (Average sense of connectedness with others in each state; standardized). Use this dataset to answer the following questions: (a) It has been hypothesized that self-esteem and social connectedness are both related to happiness, and that there are regional differences (North vs South) in happiness. Test these three hypotheses by examining the bivariate correlations between the three predictor variables and happiness. Report the results and interpret the correlations. [6 marks] (b) In 1 or 2 sentences, describe what you cannot learn about the relative relationships between the predictor variables (SELF, SOCIAL, SOUTH) and the outcome variable (HAPPY) from looking only at the correlations. [Put differently, why could you gain from using multiple regression to test the above listed hypotheses?] [2 marks] (c) In a multiple linear regression, test the hypothesis that these three predictor variables (SOUTH, SELF, and SOCIAL) are independently related to happiness. Describe the results of the regression model, and determine which, if any of these three variables is the best predictor of happiness in this dataset. [10 marks] (d) What, if anything, differs between the results of the correlational analysis produced in (a) and the multiple regression analysis in (c)? If there is a difference in the results of these two analyses, explain why that might be. [Hint: Compare the bivariate correlations estimated in (a) with the regression coefficients estimated in (c)]. [5 marks] (e) Check all assumptions of your regression model from question (c). Determine whether or not they have been violated, and provide evidence. If you deem an assumption to be violated, describe what you might do to address this concern. [7 marks]

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