IXL - Calculate correlation coefficients (Precalculus practice)

Find the correlation coefficient,

of the data described below.

An automobile dealership ran a radio ad campaign to help sell its least popular model. The dealership always used the same ad but broadcast it a different number of times each week.

The sales manager tallied the number of ads broadcast each week, x, and the weekly sales of the model, y.

Ads	Sales
9	1
12	4
13	9
17	8
18	19

Round your answer to the nearest thousandth.

ref_doc_title.

Learn with an example

question

Find the correlation coefficient,

of the data described below.

A botanist at a university is studying oak trees and the acorns they produce. She collected several acorns from the same tree and measured them.

For each acorn, she recorded its volume (in cubic centimeters), x, and its weight (in grams), y.

Volume (in cubic centimeters)	Weight (in grams)
1.2	1.6
1.5	1.4
1.8	5.0
1.8	1.7
2.6	6.8

Round your answer to the nearest thousandth.

key idea

The correlation coefficient,

for a set of

data points,

(

)

where

≤

measures the strength of the linear correlation of the data set. The closer

is to 1 or -1, the stronger the linear correlation of the data.

The correlation coefficient is defined by the formula:

–

(

–

)

(

–

)

where:

x
is the mean of the values
x
i
y
is the mean of the values
y
i
s
x
is the sample standard deviation of the values
x
i
s
y
is the sample standard deviation of the values
y
i
n
is the number of data points

In practice, you can use a calculator or computer to find the correlation coefficient.

solution

Each row in the table shows a data point

(

where:

the volume of an acorn (in cubic centimeters)

the weight of that book (in grams)

Use your calculator to find the correlation coefficient of the given data set:

0.855544…

≈

Round to the nearest thousandth

0.856

Round to the nearest thousandth

Looking for more? Try these:

Lesson: Correlation

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Teacher tools

Work it out

Not feeling ready yet? These can help:

GG.2Match correlation coefficients to scatter plots

Lesson: Correlation

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