IXL - Interpret regression lines (Precalculus practice)

Read the following description of a data set.

A state's Department of Education is planning to change some school district boundaries to alleviate overcrowding at certain campuses. As a first step, the department put together a report on a sample of towns in the state.

For each town in the sample, the report recorded its population (in thousands),

, and its number of schools,

The least squares regression line of this data set is:

0.016

15.154

Complete the following sentence:

If a town had one thousand more people, the least squares regression line predicts that it would have more schools.

ref_doc_title.

Learn with an example

question

Read the following description of a data set.

A software developer is looking for ways to predict how many bugs will appear in future projects. She used a bug-tracking database to analyze several recent projects.

From the database, she recorded the number of lines of code for each project,

. She also looked up the number of bugs that had been found in each project's code,

The least squares regression line of this data set is:

0.013

264.867

Complete the following sentence:

For each additional line of code, the least squares regression line predicts more bugs would be found in that project.

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 0.013 when

goes up by 1. This means:

For each additional line of code, the least squares regression line predicts 0.013 more bugs would be found in that project.

Looking for more? Try these:

Lesson: Line of best fit

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CC.12Evaluate a linear function: word problems

Lesson: Line of best fit

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