IXL - Analyze a regression line of a data set (Algebra 2 practice)

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

Sophie is preparing for the national spelling bee and is following a strict study plan. To create the plan, she timed how long it had taken her to memorize several words.

Sophie recorded the number of letters in each word, x, and how many minutes, y, it had taken her to memorize it.

Letters	Minutes
7	1
10	4
12	6
17	5
19	8

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.

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
2	17
2	17
10	15
19	20
19	20

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 times the ad airs in a week

the number of sales of the model in that week

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

(

0.181189…

)

15.915629…

Round to the nearest thousandth

0.181

15.916

Round to the nearest thousandth

Looking for more? Try these:

Lesson: Line of best fit

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Work it out

Not feeling ready yet? These can help:

SS.4Find the equation of a regression line

SS.5Interpret regression lines

Lesson: Line of best fit

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