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

If the sample data were to result in the scatterplot shown here, what is the value of the linear correlation coefficient r?

Short answer

The correlation coefficient is \(r = - 1\).

Step-by-step solution

Given information

A table provides data for two variables—enrollments in thousands and number of burglaries.

Describe the relationship between the correlation coefficient and the scatterplot

The scatterplot shows an upward straight-line pattern of observations when the correlation coefficient is 1. In case it follows a downward straight-line pattern, the coefficient measure is –1.

A random pattern results in 0 correlation.

Compute the correlation coefficient from the provided scatterplot

From the provided scatterplot, the data points are moving from the top left to the bottom right direction. Also,the data points form a straight-line pattern.

From this, it can be concluded that there is a perfect negative correlation between the variables.

Thus, the correlation coefficient is \(r = - 1\).