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1.2. Calculate the correlation of coefficient (r).

1.2. Calculate the correlation of coefficient (r).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer 1.2 legibly without using excel.

An analyst for an insurance business wishes to determine the strength of the relationship between the amount of life insurance held by families with the following results: Income per annum (R1 000) (x) Life insurance (R 1000) (y) 195 87 237 105 210 99 147 75 135 60 150 93 270 165 300 150 225 96 120 54 270 135 75 45
Transcribed Image Text:An analyst for an insurance business wishes to determine the strength of the relationship between the amount of life insurance held by families with the following results: Income per annum (R1 000) (x) Life insurance (R 1000) (y) 195 87 237 105 210 99 147 75 135 60 150 93 270 165 300 150 225 96 120 54 270 135 75 45
1.1. Draw a scatter diagram for the data above. 1.2. Calculate the correlation of coefficient (r). 1.3. Describe the relationship between the income per annum and the life insurance.
Transcribed Image Text:1.1. Draw a scatter diagram for the data above. 1.2. Calculate the correlation of coefficient (r). 1.3. Describe the relationship between the income per annum and the life insurance.
Expert Solution
Step 1

Here, Two variables are given,

X : Income per annum (in R 1000) 

Y : Life Insurance (in R 1000)

The observations X,Y is given. In order to compute the correlation coefficient we need to compute the columns XY, X2 , Y2 .

Number of observations is given by, n = 12

The Formula for correlation coefficient is given by,

r = n∑XY - ∑X∑Yn∑X2 - ∑X2×n∑Y2 - ∑Y2

X Y XY X2 Y2
195 87 16965 38025 7569
237 105 24885 56169 11025
210 99 20790 44100 9801
147 75 11025 21609 5625
135 60 8100 18225 3600
150 93 13950 22500 8649
270 165 44550 72900 27225
300 150 45000 90000 22500
225 96 21600 50625 9216
120 54 6480 14400 2916
270 135 36450 72900 18225
75 45 3375 5625 2025
ΣX = 2334 ΣY = 1164 ΣXY = 253170 ΣX2 = 507078 ΣY2 =  128376

So, We have found,

n =12

ΣX = 2334 

ΣY = 1164

ΣXY = 253170

ΣX2 = 507078

ΣY2 =  128376

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