For each of the scatterplots below:
Describe the type of linear relationship between the variables.
Estimate the value of the correlation coefficient.
Calculate the correlation coefficient for the bivariate data represented in the following tables, correct to two decimal places:
| x | 7 | 12 | 6 | 19 | 8 | 16 | 20 | 9 | 11 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 4 | 8 | 2 | 12 | 5 | 8 | 9 | 5 | 4 | 10 |
| x | 9 | 18 | 17 | 3 | 9 | 1 | 15 | 7 | 16 | 8 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 14 | 60 | 31 | 30 | 34 | 21 | 21 | 34 | 55 | 40 |
| x | 19 | 17 | 19 | 16 | 19 | 18 | 11 | 13 | 13 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 24 | 28 | 21 | 8 | -14 | 21 | 58 | 22 | 21 | 38 |
| x | 4 | 13 | 37 | 50 | 14 | 2 | 13 | 14 | 42 | 43 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | -12 | 3 | 7 | -10 | -7 | -4 | -9 | 1 | -15 | 19 |
| x | 6 | 1 | 1 | 2 | 10 | 7 | 8 | 6 | 10 | 8 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 100.4 | 99.9 | 98.9 | 100.8 | 100 | 101.3 | 97.2 | 97.4 | 100 | 100.2 |
Describe the linear relationship between the variables with the following correlation coefficients:
0.96
0.66
0.36
- 0.06
- 0.34
- 0.66
For each of the following pairs of relationships:
Determine whether the two linear relationships have the same direction.
State the relationship that has the stronger correlation.
The linear relationship between a set of data for variables x and y has a correlation coefficient of 0.3. The linear relationship between a set of data for variables x and z has a correlation coefficient of 0.9.
The linear relationship between a set of data for variables x and y has a correlation coefficient of - 0.9. The linear relationship between a set of data for variables y and z has a correlation coefficient of - 0.5.
The linear relationship between a set of data for variables x and y has a correlation coefficient of 0.8. The linear relationship between a set of data for variables s and t has a correlation coefficient of - 0.5.
The linear relationship between a set of data for variables x and y has a correlation coefficient of 0.3. The linear relationship between a set of data for variables x and t has a correlation coefficient of - 0.9.
Let r\left(x, y\right) represents the correlation coefficient for the relationship between variable x and y, and r\left(x, z\right) represents the correlation coefficient for the relationship between variables x and z.
For each of the following pairs of r\left(x, y\right) and r\left(x, z\right):
Determine whether the two linear relationships have the same direction.
State the relationship that has the stronger correlation.
r\left(x,y\right)=0.3,\, r\left(x,z\right)=0.9
r\left(x,y\right)=-0.9,\, r\left(x,z\right)=-0.5
r\left(x,y\right)=0.8,\, r\left(x,z\right)=-0.5
r\left(x,y\right)=0.3,\, r\left(x,z\right)=-0.9
For each set of bivariate data below:
Calculate the correlation coefficient to two decimal places.
Describe the strength of the relationship between the two variables.
| x | 9 | 4 | 35 | 34 | 32 | 18 | 28 | 10 | 20 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 19 | 12 | 75 | 63 | 61 | 37 | 57 | 22 | 38 | 7 |
| x | 65 | 72 | 48 | 84 | 78 | 56 | 63 | 64 | 77 | 93 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 25.5 | 24.2 | 16.8 | 10.4 | 24.8 | 9.6 | 6.3 | 21.4 | 13.7 | 16.3 |
| x | 6 | 18 | 20 | 32 | 43 | 55 | 64 | 78 | 90 | 93 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 93 | 8 | 35 | 77 | 26 | 52 | 10 | 80 | 70 | 50 |
| x | 13 | 13 | 9 | 12 | 9 | 15 | 10 | 12 | 12 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 3.6 | 12.5 | 12.1 | 12.8 | 11.1 | 9.7 | 11.4 | 9.7 | 10.6 | 8.9 |
| x | 2 | 4 | 7 | 0 | 3 | 2 | 0 | 6 | 4 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 88 | 83 | 60 | 95 | 84 | 88 | 104 | 72 | 85 | 84 |
| x | 65 | 72 | 48 | 84 | 78 | 56 | 63 | 64 | 77 | 93 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 5.5 | 4.2 | 16.8 | 10.4 | 24.8 | 9.6 | 6.3 | 21.4 | 13.7 | 16.3 |