IXL - Interpret regression lines (Geometry practice)

Read the following description of a data set.

The manager at a new bank wants to hire enough tellers to ensure no customer waits in line too long. To gather more information, he waits in line at other local banks.

At each bank the manager notes the number of teller windows that are open,

, as well as the number of minutes he has to wait in line before being served,

The least squares regression line of this data set is:

–

0.298

16.583

Complete the following sentence:

The least squares regression line predicts that for each additional open window, the time spent waiting in line decreases by minutes.

ref_doc_title.

Learn with an example

question

Read the following description of a data set.

Sidney manages the student health services department at Lowell University. She suspects that the students' poor breakfast habits are contributing to the school's academic decline. Sidney surveyed several students asking how many times they ate breakfast in the past month. She also checked each student's GPA.

The data shows the number of times each student ate breakfast in the past month,

, and his or her GPA,

The least squares regression line of this data set is:

0.017

2.032

Complete the following sentence:

If a student ate breakfast one more time in the past month, the least squares regression line predicts that their GPA 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 0.017 when

goes up by 1. This means:

If a student ate breakfast one more time in the past month, the least squares regression line predicts that their GPA would increase by 0.017.

Looking for more? Try these:

Lesson: Line of best fit

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