Suppose a university institutes a new student

retention initiative designed to increase the percentage of freshman

who return for their sophomore year. The initiative is undertaken

and they see the retention rate increase from $75\%$ to $78\%.$

Administration hails the success and rewards the retention staff with

substantial raises. Is the observed increase in retention rates

compelling evidence to warrant the raises? What are the weaknesses

of this evidence and how could regression analysis help address them?