Describe correlation

EXAMPLE 1

Telephones

Describe the correlation shown by each scatter plot.

Describe correlation

EXAMPLE 1

SOLUTION

The first scatter plot shows a positive correlation, because as the number of cellular phone subscribers increased, the number of cellular service regions tended to increase.

The second scatter plot shows a negative correlation, because as the number of cellular phone subscribers increased, corded phone sales tended to decrease.

EXAMPLE 2 Estimate correlation coefficients

Tell whether the correlation coefficient for the data isclosest to – 1, – 0.5, 0, 0.5, or 1. a.

SOLUTION

a. The scatter plot shows a clear but fairly weak negative correlation. So, r is between 0 and – 1, but not too close to either one. The best estimate given is r = – 0.5. (The actual value is r – 0.46.)

Estimate correlation coefficients

EXAMPLE 2

b. The scatter plot shows approximately no correlation. So, the best estimate given is r = 0. (The actual value is r – 0.02.)

SOLUTION

b.

Estimate correlation coefficients

EXAMPLE 2

c.

c. The scatter plot shows a strong positive correlation. So, the best estimate given is r = 1. (The actual value is r 0.98.)

SOLUTION

GUIDED PRACTICE for Examples 1 and 2

For each scatter plot, (a) tell whether the data have a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient is closest to –1, – 0.5, 0, 0.5, or 1.

1.

GUIDED PRACTICE for Examples 1 and 2

SOLUTION

(a) The scatter plot shows a positive correlation.

(b) The best estimate given is r = 0.5.

GUIDED PRACTICE for Examples 1 and 2

For each scatter plot, (a) tell whether the data have a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient is closest to –1, – 0.5, 0, 0.5, or 1.

2.

GUIDED PRACTICE for Examples 1 and 2

SOLUTION

(a) The scatter plot shows a strong negative correlation. So the best estimate given is r is–1.

(b) The best estimate given is r = –1.

GUIDED PRACTICE for Examples 1 and 2

For each scatter plot, (a) tell whether the data have a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient is closest to –1, – 0.5, 0, 0.5, or 1.

3.

GUIDED PRACTICE for Examples 1 and 2

SOLUTION

(a) The scatter plot shows approximately no correlation.

(b) The best estimate given is r = 0.