1. We will examine the effect of selectivity (medium vs high) of a university that a studentgraduates from has on their income 20 years later. We also consider the individuals’socio-economic background (low, medium, high). Assume that these students all hadsimilar SAT scores and high school GPAs. While this data is simulated, it based onactual research. The data set for this problem is University which has the responsevariable Income (yearly income in dollars) with covariate Selectivity which measurestheir alma-mater’s selectivity and Socio which measures their socio-economicbackground.(a) Build an appropriate model.(b) Summarize the effect of socio-economic status and college selectivity on income.(c) For a person with low socio-economic background, give a confidence interval forthe increase in income for attending a high selectivity university compared to amedium selectivity university.(d) Give an estimate and confidence interval for the difference in income betweena person of high socio-economic background who went to a medium selectivityschool vs a person of medium socio-economic background that went to a highlyselective school.
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