Question

All brawn? The following scatterplot plots the average brain weight (in grams) versus average body weight (in kilograms) for $96$ species of mammals.$18$ There are many small mammals whose points overlap at the lower left.

a. The correlation between body weight and brain weight is $r=0.86$ Interpret this value.

b. What effect does the human have on the correlation? Justify your answer.

Short answer

Part (a) There is a fairly strong and positive association between body weight $(inkg)$and brain weight $(ing)$

Part (b) The correlation coefficient $r$ would decrease due to a decrease in linearity.

Step-by-step solution

Part (a) Step 1: Given information

Correlation, $r=0.86$

Part (a) Step 2: Explanation

A positive linear correlation exists when $r$ is positive.

A negative linear correlation exists when $r$ is negative.

For weak correlation,

$0<\left|r\right|<0.5$

For moderate correlation,

$0.5<\left|r\right|<0.8$

For strong correlation,

$0.8<\left|r\right|<1$

Note that

The association between body weight in kilograms and brain weight in grams is a strong and positive association.

Part (b) Step 1: Explanation

Note that

The dot corresponding to "Human" in the scatterplot is above the typical pattern in the other points.

Thus,

In comparison to other mammals, humans have a larger brain weight in proportion to their body weight.

Also,

Because of the divergence from the linear pattern, the data's linearity is reduced.

We also know

The correlation measures the degree of linearity between the variables.

Hence,

Due to a decrease in linearity, the correlation coefficient$r$ would also decrease.