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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Determining Correlation In Exercises 19-24, plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of r and confirm your result. The number r is called the correlation coefficient. It is a measure of how well the model fits the data. Correlation coefficients vary between -1 and 1, and the closer |r| is to 1, the better the model.

Chapter 7.7, Problem 24E, Determining Correlation In Exercises 19-24, plot the points and determine whether the data have

(0.5, 2), (0.75, 1.75), (1, 3), (1.5, 3.2), (2, 3.7), (2.6, 4)

To determine

Plot the given points (0.5,2),(0.75,1.75),(1,3),(1.5,3.2),(2,3.7),(2.6,4) and determine about whether the data have positive, negative or no linear correlation. Use graphing utility to find the value of r and confirm your result.

Explanation

Given Information:

The points are given as, xi=0.5,0.75,1,1.5,2,2.6  and  yi=2,1.75,3,3.2,3.7,4 respectively.

Formula Used:

For the computation of correlation coefficient r, use the formula as,

r=nxiyixiyin(x2)(x)2n(y2)(y)2

Table for computation is as below.

Sl.no xi yi xi2 yi2 xiyi
1 0.5 2 0.25 4 1
2 0.75 1.75 0.5625 3.06 1.3125
3 1 3 1 9 3
4 1.5 3.2 2.25 10.24 4.8
5 2 3.7 4 13.69 7.4
6 2

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