IXL - Find the equation of a regression line (Precalculus practice)

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

A gym franchise was considering a television marketing campaign to increase its membership. The franchise's market researchers wanted to get a better sense of the television and exercise habits of the gym's target demographic. To begin, the market researchers surveyed some of the current members about how many hours they had spent watching television and exercising last month.

Using the survey responses, the researchers compared the number of hours of television watched, x, to the number of hours of exercise, y, for each member.

Hours of television	Hours of exercise
10	31
17	48
37	21
38	8
43	56

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.

Andrew wants to ensure that the new board game he's designing is accessible to a wide age range. To test this, he had several children of various ages play the board game against each other. Each child played the game the same number of times.

For each child, Andrew recorded his or her age, x, and the number of games that child had won, y.

Age	Games won
8	1
10	4
10	7
11	7
11	9

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 age of a child

the number of games that child won

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

(

2.333333…

)

–

17.733333…

Round to the nearest thousandth

2.333

–

17.733

Round to the nearest thousandth

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Lesson: Line of best fit

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