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

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

Grape growers in France think they will have a massive crop this year and want to know how this will influence demand for grape juice.

They compared how many grapes were produced (in millions of metric tons), x, and the amount of French grape juice that was sold in previous years (in billions of liters), y.

Grape production	Grape juice sold
3.1	5.5
4.0	5.4
4.3	5.3
5.5	5.8
6.0	5.9

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 professor wants to know if a student's first exam score can be used to accurately predict his or her final exam score.

She looked at how some of her previous students did on their first exam, x. She also looked at their final exam scores, y. Both exams were graded out of 100.

First exam score	Final exam score
49	49
52	67
71	75
78	69
94	77

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:

a student's first exam score

that student's final exam score

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

(

0.460680…

)

35.705175…

Round to the nearest thousandth

0.461

35.705

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:

GG.4Find the equation of a regression line

GG.5Interpret regression lines

Lesson: Line of best fit

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