3. Can SAT scores predict college performance? Let x be a variable that represents SAT score of a computer science major, and let y be a variable that represents a student's GPA upon graduation. A random sample of n =15 computer science majors provided their SAT scores and GPAs. The scatter diagram for the SAT score and GPA is given below:

Let =17,595,

2=20,741,103,

=46,2=143

=54,150.07.

The sample means and sample standard deviations are =1173,=3.05,=85 and =0.5.

(a) Find the sample correlation coefficient r. Truncate to two decimal places. What does the value tell you about the data?

(b) Find the equation of the least squares line =+. Truncate to four decimal places. What does the slope mean?

(c) Find the value of the coefficient of determination 2. Truncate to two decimal places. What does this number mean?

(d) What is the predicted GPA if a computer science major got a 1140 on the SAT? Truncate to two decimal places.