IXL | Find the equation of a regression line

Find the equation for the least squares regression line of the data described below.

The owner of a bicycle store wonders if the employees who take the longest lunch breaks also make the fewest bicycle sales.

One day, he notes the length of each salesperson's lunch break (in minutes), x, as well as the number of bicycles he or she sold that day, y.

Length of lunch break (in minutes)	Bicycles
26	6
27	8
42	4
45	4
50	4

Round your answers to the nearest thousandth.

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Learn with an example

question

Find the equation for the least squares regression line of the data described below.

Eddie wants to attract more customers to his family's hardware store, so he is investigating whether revamping the store's advertising campaign would help.

To find out, Eddie kept data from the past several weeks on the number of 30-second advertisements he had purchased, x, and the number of customers who had visited his store, y.

Advertisements	Customers
6	48
7	75
9	65
13	89
14	44

Round your answers to the nearest thousandth.

key idea

A line can be used to predict values based on a data set. You can look at residuals to see how well a line fits the data. Residuals are the differences between the observed values and the values predicted by the line.

The least squares regression

line,

is the line for which the sum of the squares of the residuals is minimized. It is commonly used to make predictions for a data set.

In practice, you can use a calculator or computer to find the equation of the regression line.

solution

Each row in the table shows a data point

(

where:

the number of advertisements purchased in a given week

the number of customers who visit the store during that week

Use your calculator to find the equation of the least squares regression line for the given data set:

(

0.496062…

)

59.338582…

Round to the nearest thousandth

0.496

59.339

Round to the nearest thousandth

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Lesson: Line of best fit

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