Question

# Construct a scattergram for each data set. Then calculate r and r2 for each data set....

Construct a scattergram for each data set. Then calculate r and r2 for each data set. Interpret their values. Complete parts a through d.

 x y a. −1 0 1 2 3 −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.)

 x y b. −1 0 1 2 3 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.)

 x y b. negative 1−1 00 11 22 33 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.

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.​

​​​​​​​

​​​​​​​

​​​​​​​

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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