The current workforce is dominated by "Generation Y"-people born between 1982 and 1999. These workers have a reputation as having an entitlement mentality (e.g., they believe they have a right to a high-paying job, without the work ethic). The reasons behind this phenomenon were investigated in Proceedings of the Academy of Educational Leadership (Vol. 16, 2011). A sample of 272 undergraduate business students was administered a questionnaire designed to capture the behaviors that lead to an entitlement mentality. The responses were used to measure the following two quantitative variables for each student: entitlement score (y) - where higher scores indicate a greater level of entitlement, and "helicopter parents" score (x) - where higher scores indicate that the student's parents had a higher level of involvement in his or her everyday experiences and problems.
a. Give the equation of a simple linear regression model relating y to x.
b. The researchers theorize that helicopter parents lead to an entitlement mentality. Based on this theory, would you expect β0, to be positive or negative (or are you unsure)? Would you expect β1 to be positive or negative (or are you unsure)? Explain.
c. The p-value for testing H0: β1 = 0 versus Ha: β1 > 0 was reported as .002. Use this result to test the researchers' entitlement theory at α = .01.