IXL - Analyze a regression line of a data set (Algebra 1 practice)

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

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

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

Hours of video games	Hours of sleep
0.2	9
0.8	10
1.7	5
2.4	6
3.6	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 team of forestry specialists from the Swift lumber company visited a section of the forest that was going to be logged for timber. They took measurements to evaluate the health and growth of trees in the area.

The team counted the number of rings on several trees to find their ages (in years), x. They also measured the diameter of these trees (in meters), y.

Age (in years)	Diameter (in meters)
27	1.4
39	2.2
51	2.7
76	2.7
96	2.8

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 tree (in years)

the diameter of that tree (in meters)

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

(

0.016968…

)

1.379234…

Round to the nearest thousandth

0.017

1.379

Round to the nearest thousandth

Looking for more? Try these:

Lesson: Line of best fit

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Not feeling ready yet? These can help:

N.8Write a linear function: word problems

JJ.5Write equations for lines of best fit

Lesson: Line of best fit

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