Thirteen students entered the business program at Sante Fe College 2 years ago.

Question

Thirteen students entered the business program at Sante Fe College 2 years ago. The following table indicates what each student scored on the high school SAT math exam and their grade-point averages (GPAs) after students were in the Sante Fe program for 2 years Student Sat Score 421 377 585 690 608 390 415 GPA 2.90 2.93 3.00 3.45 3.66 2.88 2.15 Student Sat Score 481 501 613 709 366 GPA 2.53 3.22 1.99 2.75 3.90 1.60 a. Is there a meaningful relationship between SAT math scores and grades? b. If a student scores a 350, what do you think his or her GPA will be? c. What about a student who scores 800?

Explanation / Answer

We will try to establish the answer using linear regression equation.

Let,

G = A + B.S

Where,

S ( independent variable ) = SAT score

G ( dependent variable )= GPA

A, B = Constants

We will place all values of GPA and SAT scores as given in two separate columns in excel and apply the formula LINEST ( ) . Accordingly, we get :

A = 1.027

B = 0.0034

Thus, the linear regression equation is :

G = 1.027 + 0.0034.S

Answer to question # b and # c:

Corresponding GPA for a SAT score of 350 = 1.027 + 0.0034 x 350 = 1.027 + 1.19 = 2.217

Corresponding GPA for a SAT score of 800 = 1.027 + 0.0034 x 800 = 1.027 + 2.72 = 3.747

We also find out Correlation coefficient between Sat score and GPA using the formula CORREL ( ) .

Accordingly, Correlation coefficient = 0.69

Answer to question # a :

Correlation coefficient of 0.69 means that there is a positive correlation . The highest value of correlation coefficient possible is 1 . Therefore, 0.69 can be considered as a high value of correlation. Therefore, we can conclude that there is a positive and meaningful correlation between SAT scores and GPA.

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