Question

Construct a scattergram for each data set. Then calculate r and r2 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=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. This answer is correct.

Interpret r2.

97.09% of the total sample variability around y 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.

requals=negative 0.9934−0.9934

​(Round to four decimal places as​ needed.)Calculate

r squaredr2.

r squaredr2equals=. 9868.9868

​(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.

______% of the total sample variability around overbary ▼ is explained is not explained by the linear relationship between x and y. ​(Round to two decimal places as​ needed.)

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

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

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

Interpret

r squaredr2.

97.0997.09​%

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	negative 1−1	00	11	22	33
	y	55	44	22	11	negative 1−1

.

Calculate r.r=−0.9934 ​(Round to four decimal places as​ needed.)Calculater2=.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.

_______% of the total sample variability around

y overbary

is explained

is not explained

by the linear relationship between x and y.​

​​​​​​​

​​​​​​​

​​​​​​​

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.

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