IXL - Calculate correlation coefficients (Geometry practice)

Find the correlation coefficient,

of the data described below.

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

So, he looks at several houses of the same size in the area. He records the distance of each house from the ocean (in kilometers), x. He 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
6	10
7	11
7	12
11	8
19	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.

On today's episode of Science Time with Amy, Amy demonstrates that walking speed affects how wet a person will get in the rain. She simulates walking through the rain at various speeds.

Amy keeps track of her walking speed (in meters per second), x. Next, she measures how wet she is by taking the difference of her weight before and after walking through the rain (in kilograms), y.

Walking speed	Amount of water
1.1	1.9
1.2	1.9
1.5	0.6
1.6	0.9
1.6	1.5

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:

Amy's walking speed (in meters per second)

amount of water Amy soaked up on that walk ( in kilograms)

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

–

0.740888…

≈

Round to the nearest thousandth

–

0.741

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:

Match correlation coefficients to scatter plots

Lesson: Correlation

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