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Chapter 4: Q.4.134 (page 189)

Determine the linear correlation coefficient by using

a. Definition 4.8 on page 183

b. Formula 4.3 on page 185

Short Answer

Expert verified

(a) The linear correlation coefficient by using definition is 0.5

(b) The linear correlation coefficient by using Formula is0.5

Step by step solution

01

Part(a) Step 1: Given Information

Given data is

We have to obtain the linear correlation coefficient by using definition

02

Part(a) Step 2: Explanation

The linear correlation coefficient using definition is as follows

r=1n-1鈭�xi-x炉yi-y炉蟽x蟽y

The standard deviations are as follows

蟽x=1n-1鈭�(x-x炉)2蟽y=1n-1鈭�(y-y炉)2

Table of values can be computed on the following table

The standard deviations can be calculated as follows

蟽x=1n-1鈭�(x-x炉)2=13-1(2)=1

蟽y=1n-1鈭�(y-y炉)2=13-1(8)=2

The correlation coefficient can be calculated as follows

r=1n-1鈭�xi-x炉yi-y炉蟽x蟽y=13-1(2)(1)(2)=0.5

03

Part(b) Step 1: Given Information

Given data is

We have to obtain the linear correlation coefficient by using formula

04

Part(b) Step 2: Explanation 

Table of values can be computed on the following table

The linear correlation coefficient using formula is as follows

r=鈭�xy-鈭�x鈭�yn鈭�x2-鈭�x2n鈭�y2-鈭�y2n=47-9(15)3(29-(29/3))(83-(83/3))=0.5

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