Question

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

The statement is false.

Step-by-step solution

Given information

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

Describe the correlation

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

The two variables can be associated by any pattern—linear 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.