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.

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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