Question

The following indicates the number of hours that Johnny spent studying the week before each exam...

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

Homework Answers

Answer #1

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.

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