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Chapter 10: Q8CQQ (page 468)

The following exercises are based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

Enrollment (thousands)

53

28

27

36

42

Burglaries

86

57

32

131

157

True or false: If there is no linear correlation between enrollment and number of burglaries, then those two variables are not related in any way.

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Given information

A table represents the number of enrolled students (in thousands) and the burglaries for randomly selected large colleges

02

Describe the correlation

Linear correlation is a measure that finds the magnitude of linear association between two variables. The measure for Pearson鈥檚 correlation is between 鈥�1 and 1 where 1 and -1 respectively indicates perfect positive and negative linear relationships.

The two variables can be associated by any pattern鈥攍inear or non-linear.

Thus, the given statement is false as the variables can be non-linearly related if there is no linear correlation between enrollment and number of burglaries.

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