Question

A study of 60,000 college students (enrolled in 4-year programs) from around the U.S. looked at the high school GPA for each student and their College GPA at the end of their first full year of college. The following summary statistics were recorded.

Avg(x) = 3.44, SDx = 0.66, Avg(y) = 3.25, SDy = 0.77, r = 0.6

where x_j =HS GPA of the j^th student and y_j =FY GPA of the j^th student.

Based on this data:

(a) Find the regression equation for predicting FY GPA from HS GPA.

Show the work you did to find the equation.

(b) Find the RMS error of regression for the regression you found in (a).

Show the work you did to find the RMS error.

(c) If Kelly had a 3.0 GPA in HS, what is Kelly's FY GPA predicted to be?

Explain your reasoning.

(d) Assuming that the scatter diagram for the GPA data is ''football-shaped", what is the probability that Kelly's FY GPA will be between 3.25 and 3.75?

Show your calculations, and state clearly what assumptions you are relying on to justify these calculations.

Answer 1

​​​​​Thus Kelly's FY GPA lies between 3.25 and 3.75 is 0.24196.

In part C we used the estimated regression equation to predict FY GPA from given value of HS GPA.

To calculate RMS error of regression we use one of the formula from other formula.

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