Question

Linear Correlation Coefficient In Exercises 9–12, the linear correlation coefficient r is provided. Use Table 2-11 on page 71 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation?

Using the data from Exercise 6 “Bear Measurements,” the linear correlation coefficient is r = 0.980.

Short answer

As the given value of r equal to 0.980 does not lie within the critical values of -0.754 and 0.754, it can be concluded that there is a linear correlation between chest size and the weight of the bears.

Step-by-step solution

Given information

The value of the correlation coefficient between the two variables, chest size (in inches) and weight (in lb), is r = 0.980.

Refer to Exercise 6 for the sampled number of bears, which is 7(n).

Significance of correlation

The critical values are compared to the correlation coefficient measures to determine the linear correlation between variables.

Two cases are possible:

• If the computed value of r within the range of -critical value and +critical value , it can be said that the correlation is insignificant. This means that there is no linear correlation between the two variables.

• If the computed value of r does not lie within the range of -critical value (r) and +critical value (r), it can be said that the correlation is significant. This means that there exists a linear correlation between the two variables.

Comparison of the given value

The value of r between chest size and weight is equal to 0.980.

The number of data pairs is 7

Refer to Table 2-11 corresponding to the seven data pairs for obtaining the critical value as 0.754.

Since the given value of r lies beyond the interval of -0.754 and +0.754, it can be said that there is a linear correlation between chest size and the weight of bears.