IXL - Interpret regression lines (Algebra 1 practice)

Read the following description of a data set.

A television sports commentator recently declared that basketball teams that rely on the three-point shot cannot win championships. To see if the commentator had a valid point, a sports analyst reviewed game statistics from several teams over the past season.

For each of the teams, the analyst calculated what percentage of attempted field goals had been three-pointers,

, and the number of wins in the season,

The least squares regression line of this data set is:

2.413

–

12.264

Complete the following sentence:

If a team increased their percentage of three-point shots by one, the least squares regression line predicts they would have won more games in the season.

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Learn with an example

question

Read the following description of a data set.

Ellie is an aspiring journalist who writes a music blog. In her latest post, she examined how critical acclaim and commercial success were related for recently released albums. To judge critical acclaim, she looked up the albums on a site that combines ratings from multiple critics into a single number from 0 to 100.

Ellie recorded the score,

, and the sales,

, of each album.

The least squares regression line of this data set is:

4,334.017

–

325,578.593

Complete the following sentence:

For each additional point in an album's score, the least squares regression line predicts that its sales would increase by

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.

solution

You can use the least squares regression line to predict the

-value

for a given

-value.

The slope of the regression line is the predicted change in the

-value

when the

-value

increases by 1.

So, the least squares regression line predicts the

-value

will go up by 4,334.017 when

goes up by 1. This means:

For each additional point in an album's score, the least squares regression line predicts that its sales would increase by 4,334.017.

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Lesson: Line of best fit

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