Question

In: Statistics and Probability

1) Thirteen student were admitted to the undergraduate business program at Whatsamatta University 2 years ago....

1) Thirteen student were admitted to the undergraduate business program at Whatsamatta University 2 years ago. The following table indicates what their grade-point average was after 2 years at the University. Also listed is their SAT score that they scored when they were in high school (maximum score is 2400).

Student

SAT Score

GPA

Student

SAT Score

GPA

A

1263

2.90

H

1443

2.53

B

1131

2.93

I

2187

3.22

C

1755

3.00

J

1503

1.99

D

2070

3.45

K

1839

2.75

E

1824

3.66

L

2127

3.90

F

1170

2.88

M

1098

1.60

G

1245

2.15

a) Using the SAT score to predict their GPA is there a meaningful relationship between the SAT score and their GPA? How do you know?

b) If a student has a SAT score of 1200, what do you think their GPA will be in two years?

c) If a student has a SAT score of 2400, what do you think their GPA will be in two years?

Solutions

Expert Solution

Thirteen student were admitted to the undergraduate business program at Whatsamatta University 2 years ago. The following table indicates what their grade-point average was after 2 years at the University and their SAT score that they scored when they were in high school (maximum score is 2400).

STUDENT SAT SCORE(X) GPA(Y)
A 1263 2.90
B 1131 2.93
C 1755 3.00
D 2070 3.45
E 1824 3.66
F 1170 2.88
G 1245 2.15
H 1443 2.53
I 2187 3.22
J 1503 1.99
K 1839 2.75
L 2127 3.90
M 1098 1.60

a) Now we want to check is there present any meaningful relationship between SAT score and GPA for which we use students SAT score to predict the students GPA. Here meaningful relation means is there present high correlation or not and if there present a good correlation between SAT score and GPA then we easily say that SAT score is a good predictor to predict GPA.

now we define SAT score by X(independent variable) and GPA by Y(dependent variable). now correlation between SAT score(X) and GPA(Y) is given by the formula,

   

Xi(SAT score) Yi(GPA) Xi- Yi- (Xi-)(Yi-) (Xi-)2 (Yi-)2
1263 2.90 -325.846 0.057 -18.573 106176 0.00325
1131 2.93 -457.846 0.087 -39.833 209623 0.00757
1755 3.00 166.1534 0.157 26.086 27607 0.02465
2070 3.45 481.1534 0.607 292.060 231509 0.36845
1824 3.66 235.154 0.817 192.121 55297 0.66749
1170 2.88 -418.846 0.037 -15.497 175432 0.00137
1245 2.15 -343.846 -0.693 238.285 118230 0.48025
1443 2.53 -145.846 -0.313 45.650 21271 0.09797
2187 3.22 598.154 0.377 225.504 357788 0.14213
1503 1.99 -85.846 -0.853 73.227 7370 0.72761
1839 2.75 250.154 -0.093 -23.264 62577 0.00865
2127 3.90 538.154 1.057 568.829 289610 1.11725
1098 1.60 -490.846 -1.243 610.122 240930 1.54505

from the table we see that ,

So we get the correlation between SAT score(X variable) and GPA(Y variable) is 0.6918 which is good. So SAT score is a good predictor of GPA.

b) Now we want to find the GPA score of a particular student if the student has SAT score 1200.

for this purpose we established the linear regression equation of " GPA on SAT score ". And the regression equation is given by ,

=> GPA = a + b SAT score

c) Now if a student has SAT score 2400 then GPA score of this student is given by,

GPA = 1.0246 + 0.001143 2400 = 3.7678


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