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

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

Every summer, the Centerville Fair has a grasshopper catching contest. Grasshoppers are released into a fenced area, and participants are given five minutes to catch as many as they can. To even the playing field, the organizers developed a handicap system based on the results of this year's competition. The system takes into account the different experience levels of the contest participants.

To create the system, the organizers recorded the number of times each contestant had previously participated, x, and the number of grasshoppers each contestant had caught this year, y.

Grasshopper contest statistics

The mean of the x-values is
9.011
.
The mean of the y-values is
19.275
.
The sample standard deviation of the x-values is
6.902
.
The sample standard deviation of the y-values is
16.523
.
The correlation coefficient of the data set is
0.714
.

Round your answers to the nearest thousandth.

ref_doc_title.

Learn with an example

question

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

Elena's baseball card collection includes sets from many different seasons. Her older sets seem to be missing more cards than the newer sets, so she investigated to see whether this was actually the case.

For each set, she recorded the number of years since its release, x, and the number of missing cards, y.

Baseball cards statistics

The mean of the x-values is
11.668
.
The mean of the y-values is
31.143
.
The sample standard deviation of the x-values is
3.572
.
The sample standard deviation of the y-values is
5.812
.
The correlation coefficient of the data set is
0.745
.

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.

The slope,

and

-intercept,

of the least squares regression line for the data set,

(

where

≤

are given by the following formulas:

–

where:

x
is the mean of the values
x
i
y
is the mean of the values
y
i
s
x
is the sample standard deviation of the values
x
i
s
y
is the sample standard deviation of the values
y
i
r
is the correlation coefficient of the data points
(
x
i
,

y
i
)

solution

First, find the slope of the regression line.

0.745

5.812

3.572

1.212189…

Then, find the

-intercept.

–

31.143

–

(

1.212189…

)

11.668

16.999175…

Round the slope,

and the

-intercept,

to the nearest thousandth. The equation of the least squares regression line is:

1.212

16.999

Looking for more? Try this:

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

GG.4Find the equation of a regression line

GG.5Interpret regression lines

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!