Question

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

T

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 coefficient of determination.

a) 0.9861; There is a strong positive relationship between the variables.

b) 0.9724; Approximately 97% of the variation in exam score is explained by the LSRL.

c) 0.9724; There is a strong positive relationship between the variables.

d) 0.9861; Approximately 99% of the variation in exam score is explained by the LSRL.

e) −0.9861; There is a strong negative 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

a) 0.9861; There is a strong positive relationship between the variables.

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