The following indicates the number of hours that Johnny spent
studying the week before each exam in his classes along with the
corresponding exam scores:
Hours
Studying: 4 5 8 12 15 19
Score on Exam: 54 49
60 70 81 94
Find and interpret the correlation coefficient.
a) −0.9861; There is a strong negative relationship between the variables.
b) 0.9861; There is a strong positive relationship between the variables.
c) 0.9724; Approximately 97% of the variation in exam score is explained by the LSRL.
d) 0.9861; Approximately 99% of the variation in exam score is explained by the LSRL.
e) 0.9724; There is a strong positive relationship between the variables
Solution :
X | Y | XY | X^2 | Y^2 |
4 | 54 | 216 | 16 | 2916 |
5 | 49 | 245 | 25 | 2401 |
8 | 60 | 480 | 64 | 3600 |
12 | 70 | 840 | 144 | 4900 |
15 | 81 | 1215 | 225 | 6561 |
19 | 94 | 1786 | 361 | 8836 |
n | 6 |
sum(XY) | 4782.00 |
sum(X) | 63.00 |
sum(Y) | 408.00 |
sum(X^2) | 835.00 |
sum(Y^2) | 29214.00 |
Numerator | 2988.00 |
Denominator | 3030.12 |
r | 0.9861 |
r square | 0.9724 |
Xbar(mean) | 10.5000 |
Ybar(mean) | 68.0000 |
SD(X) | 5.3774 |
SD(Y) | 15.6525 |
b | 2.8703 |
a | 37.8617 |
r = 0.9861
b) 0.9861; There is a strong positive relationship between the variables.
Get Answers For Free
Most questions answered within 1 hours.