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.

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.  answer is correct.

Interpret r2.

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

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

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 ove rbar 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

r squaredr2.

98.6898.68​%

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.

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.  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 over bar y 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

SOLUTION-  I am using just SPSS software below are drawn scatter diagram

Ans(a)- option (D) is correct there is very strong linear relation b/w x and y.

explaination- Notice that the Y increases as the X increases. We can see this easily by drawing a trend line that best fits all your data points. Notice that the trend line is pointing in the north east direction, which means it has a positive slope. This indicates that a positive relationship exists between X and Y.

In other words we can say coefficient of determination, denoted R² =0.971  tells that the proportion of the variance in the dependent variable Y that is 97.1% predictable from the independent variable(s) X.

Ans(b) - Option(A) is correct.

there is a very strong negative linear relationship b/w x and y.

Explaination- A scatter diagram showing a negative relationship has a downward trend. In other words, the slope of the best-fit trend line is negative or pointing in the south east direction, like in the image below.

In other words we can say coefficient of determination, denoted R² =0.987 tells that the proportion of the variance in the dependent variable Y that is 98.7% predictable from the independent variable(s) X.

Ans(c)- Option(D) is correct.

there is no relationship b/w x and y.

Explaination- value of correlation coefficient r= 0

If the data points on a scatter diagram do not seem to have any kind of linear positive or negative trend, then there is no linear relationship b/w the variable.In other words we can say coefficient of determination, denoted R² =0 tells that the proportion of the variance in the dependent variable Y that is not predictable from the independent variable(s) X.