In: Statistics and Probability
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?
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