An admissions officer claims that at his college the regression equation ŷ = 0.5 + 7x approximates the relationship between y = college GPA and x = high school GPA, both measured on a four point scale.
a. Sketch this equation between x = 0 and 4, labeling the x - and y -axes. Is this equation realistic? Why or why not?
b. Suppose that actually ŷ = 0.5 + 0.7x. Predict the GPA for two students having GPAs of 3.0 and 4.0. Interpret, and explain how the difference between these two predictions relates to the slope.