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Chapter 3: Q.22 (page 162)

All brawn? The figure below plots the average brain weight in grams versus average body weight in kilograms for 96species of mammals. There are many small mammals whose points at the lower-left overlap.

(a) The correlation between body weight and brain weight isr=0.86. Explain what this value means.

(b) What effect would removing the elephant have on the correlation? Justify your answer.

Short Answer

Expert verified

a). Body weight in kilogram and brain weight in gram have a very significant positive relationship.

b). Ther coefficient of linear correlation would decrease.

Step by step solution

01

Part (a) Step 1: Given Information 

The average brain weight in grams versus average body weight in kilograms for 96 species of mammals.

02

Part (a) Step 2: Explanation

The stronger the positive relationship, the closer the correlation, r, is to 1.

Body weight in kilogram and brain weight in gram have a very significant positive relationship.

03

Part (b) Step 1: Given Information 

The average brain weight in grams versus average body weight in kilograms for 96species of mammals.

04

Part (b) Step 2: Explanation

The point in the top right corner (Elephants) follows the same basic linear trend as the rest of the scatterplot's data points.

When this point is removed from the data set, the data appears less linear, and the linear correlation coefficient rdecreases.

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