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.
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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