Question

This does not copy well! Looking for the Correlation coefficient by hand.

For the accompanying data​ set, (a) draw a scatter diagram of the​ data, (b) by​ hand, compute the correlation​ coefficient, and​ (c) determine whether there is a linear relation between x and y.

data set.

x - 2 4 6 6 7

y - 4 8 11 12 19

Click here to view the critical values table.

LOADING...

​(a) Draw a scatter diagram of the data. Choose the correct graph below.

A.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 2. The following 5 points are plotted, listed here from left to right: (2, 19); (4, 12); (7, 11); (7, 8); (8, 4).

B.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 1. The following 5 points are plotted, listed here from left to right: (2, 4); (4, 8); (7, 11); (7, 7); (8, 19).

C.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 2. The following 5 points are plotted, listed here from left to right: (2, 4); (4, 8); (7, 11); (7, 12); (8, 19).

D.

010020xy

A scatter diagram has a horizontal x-axis labeled from 0 to 10 in increments of 1 and a vertical y-axis labeled from 0 to 20 in increments of 1. The following 5 points are plotted, listed here from left to right: (2, 19); (4, 7); (7, 11); (7, 8); (8, 4).

​(b) By​ hand, compute the correlation coefficient.

The correlation coefficient r is: ________

​(Round to three decimal places as​ needed.)

​(c) Determine whether there is a linear relation between x and y.

Because the correlation coefficient is negative/ positive and the absolute value of the correlation​ coefficient,nothing​,( Greater or not Greater) Than the critical value set is _______

not greater

greater

than the critical value for this data​ set,

nothing​,

▼

no

a negative

a positive

linear relation exists between x and y.

​(Round to three decimal places as​ needed.)

Answer 1

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	2	4	9.0000	46.24	20.4000
2	4	8	1.0000	7.84	2.8000
3	6	11	1.0000	0.04	0.2000
4	6	12	1.0000	1.44	1.2000
5	7	19	4.0000	67.24	16.4000
Total	25	54	16.0000	122.80	41.0000
Mean	5.000	10.80	SSX	SSY	SXY

correlation coefficient r=

Sxy/(√Sxx*Syy) =41/sqrt(16*122.80) =

0.925

Because the correlation coefficient is positive and the absolute value of the correlation​ coefficient, 0.925 Greater Than the critical value set is 0.878

a positive linear relation exists between x and y.