Chapter 3.1, Problem 20E

(a)

To determine

Interpretation of correlation for the relationship between body weight and brain weight.

Answer to Problem 20E

There is fairly strong and positive association between body weight (in kg) and brain weight (in g).

Explanation of Solution

Given information:

Correlation,

  $r=0.86$

  

When r is positive, positive linear correlation exists.

When r is negative, negative linear correlation exists.

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 strong and positive association.

(b)

To determine

Effect of human on the correlation.

Answer to Problem 20E

The correlation coefficient r would decrease due to decrease in linearity.

Explanation of Solution

Given information:

Correlation,

  $r=0.86$

  

Note that

In the scatterplot, the dot corresponding to “Human” lies above the general pattern in the other points.

Thus,

The humans have a higher brain weight relative to their body weight in comparison with other mammals.

Also,

The amount of linearity in the data gets decreased due to its deviation from the linear pattern.

We also know

The amount of linearity between the variables is measured by the correlation.

Hence,

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