Question

x	y
23	28
17	20
8	2
29	22
12	18

Use the sample data above to answer the following question.  (See exercise 56 on page 160 of your textbook for a similar problem.)

Compute the correlation.

Answer 1

Sol:

Formula for r is

x	y	xbar	y bar	x-xbar	y-ybar	(x-xbar)(y-ybar)	(x-xbar)^2	(y-ybar)^2
23	28	17.8	18	5.2	10	52	27.04	100
17	20	17.8	18	-0.8	2	-1.6	0.64	4
8	2	17.8	18	-9.8	-16	156.8	96.04	256
29	22	17.8	18	11.2	4	44.8	125.44	16
12	18	17.8	18	-5.8	0	0	33.64	0
						252	282.8	376
xbar=sumx/n=89/5=17.8
ybar=sumy/n=90/5=18
				r=252/sqrt(282.8*376)
				r=0.7728

Alternatively you can find r using software:

install analysis tool pack in excel

go to data>data analysis>correlation

you get

	x	y
x	1
y	0.7728	1

correlation coefficient=r=0.7728

There exists a strong positive relationship between x and y