According to the World Health Organization, the health of an individual, to a large extent, is determined by factors such as income, education, genetics, and social connections. In a survey, 120 American adults are asked how they rated their health (Health) and social connections (Social) on a scale of 1 to 100. Information is also gathered on their household income (Income, in $1,000s), and college education (College equals 1 if they have completed bachelor’s degree, 0 otherwise). A portion of the data is shown in the accompanying table. 

a. Estimate and interpret a regression model for Health using Social, Income, and College as the predictor variables. Predict the health rating of a college-educated person given Social = 80 and Income = 100. What if the person is not college-educated? 

b. Estimate and interpret an extended model that includes the interactions of Social with Income and Social with College. Predict the health rating of a college-educated person given Social = 80 and Income = 100. What if the person is not college-educated? 

c. Explain which of the above two models is preferred for making predictions.

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Health 52 55 ⠀ 58 Social 58 68 ⠀ 90 Income 80 43 ⠀ 35 College 0 0 1 0