Numerous studies have shown that watching too much television hurts school grades. Others have argued that television is not necessarily a bad thing for children (Mail Online, July 18, 2009). Like books and stories, television not only entertains, it also exposes a child to new information about the world. While watching too much TV is harmful, a little bit may actually help. Researcher Matt Castle gathers information on the grade point average (GPA) of 28 middle school children and the number of hours of TV they watched per week. A portion of the data is shown in the accompanying table; the complete data, labeled Television, is found on the text website.
a. Estimate a quadratic regression model where the GPA of middle school children is regressed on hours and hourssquared.
b. Is the quadratic term in this model justified? Explain.
c. Find the optimal number of weekly hours of TV for middle school children.