In an attempt to raise the low graduation rates of college football and basketball players, Division I institutions require that prospective athletes must meet new grade point aver- age (GPA) standards (based on a maximum of 4.0) to play as freshmen, and enrolled athletes must meet these new standards to keep playing (see Table 35).

Let G be the qualifying core GPA for an SAT score of s points.
a. Use technology to construct a scatterplot.
b. Describe the four characteristics of the association. Compute and interpret r as part of your analysis.
c. Use technology to graph the model G = - 0.00254s + 4.58 on the scatterplot. Does the line come close to the data points?
d. If one athlete€™s SAT score is 200 points higher than another athlete€™s SAT score, estimate how much lower the qualifying core GPA is for the student with the higher SAT score.
e. If an athlete€™s SAT score is 400 points, the lowest pos- sible score, predict the student€™s qualifying core GPA. The actual qualifying core GPA is 3.55. Compute the error in your prediction. Did you perform extrapolation or interpolation?

Transcribed Image Text:

Table 35 Core GPAs Needed to Qualify to Play, for Given SAT Scores SAT Score Core GPA 620 700 780 860 940 1010 3.0 2.8 2.6 2.4 2.2 2.0