Question

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.

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.