Thirteen students entered the business program at Hillcrest College 2 years ago Answer

Thirteen students entered the business program at Hillcrest 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 Hillcrest program for 2 years.

Student SAT Score GPA
A 421 2.90
B 377 2.93
C 585 3.00
D 690 3.45
E 608 3.66
F 390 2.88
G 415 2.15
H 481 2.53
I 729 3.22
J 501 1.99
K 613 2.75
L 709 3.90
M 366 1.60
  1. Is there a meaningful relationship between SAT math scores and grades?

Ans:

Scatter Diagram:

 

From the 13 data points, there appears to be a positive relationship between the independent variable (SAT math scores) and the dependent variable (grades): As SAT math scores increases, grades (GPA) tend to be higher.

  1. If a student scores a 350, what do you think his or her GPA will be?

Ans:

Student SAT Score GPA x2 y2 xy
A 421 2.9 177241 8.41 1220.9
B 377 2.93 142129 8.5849 1104.61
C 585 3 342225 9 1755
D 690 3.45 476100 11.9025 2380.5
E 608 3.66 369664 13.3956 2225.28
F 390 2.88 152100 8.2944 1123.2
G 415 2.15 172225 4.6225 892.25
H 481 2.53 231361 6.4009 1216.93
I 729 3.22 531441 10.3684 2347.38
J 501 1.99 251001 3.9601 996.99
K 613 2.75 375769 7.5625 1685.75
L 709 3.9 502681 15.21 2765.1
M 366 1.6 133956 2.56 585.6
           
Σx/n 529.62        
Σy/n   2.84      
Σx2     3857893    
Σxy         20299
Σy2       110.2718  
b 0.003        
a 1.028        
           
r ( Correlation Coefficient)   0.692      
           
coefficient of determination (r2)   0.479      

We can find a mathematical equation by using the least-squares regression approach:

The estimated regression equation, therefore, is:

Y = 1.028 + 0.003 *X

  Putting a value of x= 350 in the regression equation will give

y = 1.028 + 0.003 *350 = 2.078

If a student scores a 350, his or her GPA = 2.078

  1. c) What about a student who scores 800?

Y = 1.028 + 0.003 *X

  Putting a value of x= 800 in the regression equation will give

y = 1.028 + 0.003 *800 = 3.428

If a student scores a 800, his or her GPA = 3.428