Question

Construct a scattergram for each data set. Then calculate r and r 2 for each data set. Interpret their values. Complete parts a through d

a.	x	−1	0	1	2	3
	y	−3	0	1	4	5

Calculate r.

r=. 9853 ​(Round to four decimal places as​ needed.)

Calculate r2.

r2=0.9709. ​(Round to four decimal places as​ needed.)

Interpret r. Choose the correct answer below.

A.There is not enough information to answer this question.

B.There is a very strong negative linear relationship between x and y.

C.x and y are not related.

D.There is a very strong positive linear relationship between x and y. Your answer is correct.

Interpret

r2=97.09% of the total sample variability around y overbary is explained by the linear relationship between x and y.

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

b.	x	−1	0	1	2	3
	y	5	4	2	1	−1

Calculate r.

r=−0.9934 ​(Round to four decimal places as​ needed.)

Calculate r2.

r2=. 9868. ​(Round to four decimal places as​ needed.)

Interpret r. Choose the correct answer below.

A.There is a very strong negative linear relationship between x and y. Your answer is correct.

B.There is not enough information to answer this question.

C. There is a very strong positive linear relationship between x and y.

D.x and y are not related.

Interpret r2.

98.68​% of the total sample variability around y overbary is explained by the linear relationship between x and y.

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

c.	x	1	2	2	3	3	3	4
	y	2	1	3	1	2	3	2

Calculate r.

r=___________​(Round to four decimal places as​ needed.)

Answer 1

Following is the scatter plot:

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	-1	-3	1	9	3
	0	0	0	0	0
	1	1	1	1	1
	2	4	4	16	8
	3	5	9	25	15
Total	5	7	15	51	27

Sample size: n=5

The coefficient of correlation is :

The coefficient of determination is:

D.There is a very strong positive linear relationship between x and y.

The 97.09% of the total sample variability around y is explained by the linear relationship between x and y.

-----------------------

(b)

Following is the scatter plot:

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	-1	5	1	25	-5
	0	4	0	16	0
	1	2	1	4	2
	2	1	4	1	2
	3	-1	9	1	-3
Total	5	11	15	47	-4

Sample size: n=5

The coefficient of correlation is :

The coefficient of determination is:

A.There is a very strong negative linear relationship between x and y.

The 98.68​% of the total sample variability around y overbary is explained by the linear relationship between x and y.

--------------------------

(c)

Following is the scatter plot:

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	1	2	1	4	2
	2	1	4	1	2
	2	3	4	9	6
	3	1	9	1	3
	3	2	9	4	6
	3	3	9	9	9
	4	2	16	4	8
Total	18	14	52	32	36

Sample size: n=7

The coefficient of correlation is :

The coefficient of determination is:

x and y are not related.