IXL - Calculate correlation coefficients (Algebra 1 practice)

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)
3.3	2.1
3.9	2.9
5.5	3.1
5.6	3.1
5.9	1.5

Round your answer to the nearest thousandth.

ref_doc_title.

Learn with an example

question

Find the correlation coefficient,

of the data described below.

Mary works with a property developer building houses close to the coastline in Italy. Her boss thinks that demand for the houses will be based primarily on their size. Mary wants to show her boss that proximity to the ocean is also a big factor to consider.

So, she looks at several houses of the same size in the area. She records the distance of each house from the ocean (in kilometers), x. She also notes the number of people who offered to buy each house, y, when it was last put up for sale.

Kilometers from ocean	Offers
4	8
7	14
11	15
13	12
19	9

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 distance of a house to the ocean

number of offers to buy that house

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

–

0.062601…

≈

Round to the nearest thousandth

–

0.063

Round to the nearest thousandth

Looking for more? Try these:

Lesson: Correlation

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JJ.3Match correlation coefficients to scatter plots

Lesson: Correlation

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