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 8 “Heights of Fathers and Sons,” the linear correlation coefficient is r = -0.017.

Short answer

As the given value of r , -0.017, lies within the critical values of -0.632 and 0.632, it can be concluded that there is no linear correlation between the height of the father and the height of the first son.

Step-by-step solution

Given information

The value of r between the variables “height of the father” and “height of the first son” is -0.017.

Refer to Exercise 8 for the sample size of paired heights, which is 10(n)

Significance of correlation

To check whether the given linear correlation coefficient obtained from sample points is significant, the computed value of r is compared with the critical value range of r.

The decision rule for deriving a conclusion is given as follows:

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

Comparison of the given value

The computed value of the correlation coefficient between the height of the father and the height of the first son is equal to -0.017.

The number of data pairs is 10

Refer to Table 2-11 for obtaining the critical value corresponding to 10 data pairs as 0.632.

Since the given value of r lies within the interval of -0.632 and +0.632, it can be said that there is no linear correlation between the father’s height and the first son’s height.