IXL - Find the equation of a regression line (Algebra 1 practice)

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

Bryant isn't getting enough sleep and suspects it's due to playing too many video games before bed. To find out, he decided to track how much time he spends gaming.

Over several days, Bryant recorded how many hours of sleep he had gotten each night, x, as well as how many hours he had spent playing video games before bed, y.

Hours of video games	Hours of sleep
0.2	8
0.3	9
1.1	10
1.1	5
2.7	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.

A food scientist wants to understand how much sugar children like in their desserts. He sets up a study where children taste cups of vanilla pudding with varying sweetness and rate each cup on a scale of 1 to 10, where 10 is excellent.

For each tasting, the food scientist writes down the grams of sugar in the pudding cup, x, as well as its rating, y.

Grams of sugar	Rating
11	4
17	2
25	10
28	10
29	3

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 grams of sugar in a pudding cup

a child's rating of that pudding cup

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

(

0.237500…

)

0.575000…

Round to the nearest thousandth

0.238

0.575

Round to the nearest thousandth

Looking for more? Try these:

Lesson: Line of best fit

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Lesson: Line of best fit

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