In: Statistics and Probability
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.)
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.