IXL - Interpret regression lines (Algebra 2 practice)

Read the following description of a data set.

Tommy wonders how many times he has played his favorite songs on his computer. To investigate, he looked up information stored by his music playing software.

Tommy determined how long he had owned each song (in months),

. He also counted how many times each song had been played,

The least squares regression line of this data set is:

2.101

49.574

Complete the following sentence:

For each additional month owning the song, the least squares regression line predicts that it would have played more times.

ref_doc_title.

Learn with an example

question

Read the following description of a data set.

Antonio is planning a drum solo for his band's next concert. To help craft an ideal solo, he decided to compile data on his favorite drummers. He examined both their performances and their drum sets.

Antonio recorded the number of instruments in each drummer's set,

, and each drummer's typical solo length (in minutes),

The least squares regression line of this data set is:

0.538

–

5.394

Complete the following sentence:

If a drummer had one additional instrument in the set, the least squares regression line predicts that his or her typical drum solo would be minutes longer.

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 0.538 when

goes up by 1. This means:

If a drummer had one additional instrument in the set, the least squares regression line predicts that his or her typical drum solo would be 0.538 minutes longer.

Looking for more? Try these:

Lesson: Line of best fit

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