A health research institute collects information from 20 individuals on the number of years they have spent smoking cigarettes,

Question

3 years ago

8

and their age of death. The data is summarized below:
∑x=1257
∑y^2=836
∑x^2=98823
∑y=116
∑(xy)=8249

Find the correlation coefficient (r):

1 answer:

olga55 [171] · Answer 1 · 2023-01-06T06:01:45+03:00

The correlation coefficient of the health research institute data measures the relationship between the age and the years of the smokers

The correlation coefficient is 0.53

<h3>How to calculate the correlation coefficient</h3>

The correlation coefficient (r) is calculated as:

$r = \frac{n(\sum xy) - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2}}$

Using the given parameters, we have:

$r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1257^2][20 * 836 - 116^2}}$

Evaluate the exponents

$r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1580049][20 * 836 - 13456}}$

Evaluate the products

$r = \frac{164980 - 145812}{\sqrt{[1976460 - 1580049][16720 - 13456}}$

Evaluate the differences

$r = \frac{19168}{\sqrt{[396411*3264}}$

Evaluate the product

$r = \frac{19168}{\sqrt{1293885504}}$

Evaluate the root

$r = \frac{19168}{35970.6}$

Evaluate the quotient

$r = 0.53$

Hence, the correlation coefficient is 0.53

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