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Chapter 3: Q T3.6. (page 216)

Which of the following statements is not true of the correlation r between the lengths (in inches) and weights (in pounds) of a sample of brook trout?

a. r must take a value between 鈭�1 and 1.

b. r is measured in inches.

c. If longer trout tend to also be heavier, then r > 0.

d. r would not change if we measured the lengths of the trout in centimeters instead of inches.

e. r would not change if we measured the weights of the trout in kilograms instead of pounds.

Short Answer

Expert verified

The correct option is (b) r measured in inches.

Step by step solution

01

Given information

The lengths (in inches) and weights (in pounds) of a sample of brook trout were correlated (r).

02

Explanation

One of the statistical measurements of the strength of the relationship between two variables is the correlation coefficient. It does not have a specific unit. It establishes the boundaries between two numerical values of -1 and 1 It cannot be measured in any unit, including inches, and it has no effect when shifting from one unit to another, such as inches to centimeters and pounds to kilograms.

Hence, the correct option is (b)

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Most popular questions from this chapter

Actual weight Refer to Exercise 47. Use the equation of the least-squares regression line and the residual plot to estimate the actual mean weight of the infants when they were 1 month old.

When we standardize the values of a variable, the distribution of standardized values has a mean of 0 and a standard deviation of 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least squares regression line. Suppose the slope of the least-squares regression line is 20.44. We may conclude that

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