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 7 “Car Weight and Fuel Consumption,” the linear correlation coefficient is r = -0.987.

Short answer

As the given value of r equal to -0.987 does not lie within the critical values of -0.754 and 0.754, it can be concluded that there is a linear correlation between highway fuel consumption and the weight of the car.

Step-by-step solution

Given information

The value of r between the variables, highway fuel consumption (mpg) and the weight of the car, is -0.987.

Refer to Exercise 7 for the samples recorded, which is 7(n).

Significance of correlation

The computed value of the correlation coefficient is compared to the range of critical values obtained corresponding to the number of pairs of data available to derive the significance of the linear correlation between two variables.

The two cases are:

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

Comparison of the given value

The value ofr for the weight of the car and the fuel consumption is equal to -0.987.

The number of data pairs is 7.

Also, the critical value obtained from Table 2-11 corresponding to 7 data pairs is equal to 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 fuel consumption and the weight of car.