Question

Use the following information for problems 17-19:
Given the following data:

x	1	2	3	4	5	6
y	22	31	28	41	33	41

Which of the following would be the LSRL for the given data?

Determine the correlation coefficient for the data?

Find the residual value for x = 5.

Answer 1

Solution :

X	Y	XY	X^2	Y^2
1	22	22	1	484
2	31	62	4	961
3	28	84	9	784
4	41	164	16	1681
5	33	165	25	1089
6	41	246	36	1681

n	6
sum(XY)	743.00
sum(X)	21.00
sum(Y)	196.00
sum(X^2)	91.00
sum(Y^2)	6680.00
Numerator	342.00
Denominator	418.00
r	0.8182
r square	0.6694
Xbar(mean)	3.5000
Ybar(mean)	32.6667
SD(X)	1.7078
SD(Y)	6.7987
b	3.2571
a	21.2667

The correlation coefficient for the data = r = 0.8182

Predicted = 21.2667 + 5 * 3.2571 = 37.5522

Actual = 33

The residual value for x = 5. is ,

= 33 - 37.5522

= -4.5522