When points lie nearly on a line, it is useful to determine an equation for a line that lies on or comes close to the points.

Usually, there is no single line that passes through all the data points, so you try to find the line that best fits the data. This is called the best-fitting line.best-fitting line.

There are several ways to find the best-fitting line for a given set of data points. In this lesson, you will use a graphical approach.

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FITTING A LINE TO DATA

Approximating a Best-Fitting Line

DISCUS THROWS

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Write an equation of your line.

The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws.

Approximating a Best-Fitting Line

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SOLUTION

Find two points that lie on the best-fitting line,

such as (8, 138) and

(96, 230).

Find the slope of the line through these points.

(96, 230).

(96, 230)

(8, 138)

(8, 138)

9288= 1.05

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(96, 230)

(8, 138)

y = m x + b

230 – 13896 – 8

=

129.6 = b

Write slope intercept form.

Substitute 1.05 for m, 8 for x, 138 for y.

Simplify.

Solve for b.

An equation of the best-fitting line is y = 1.05 x + 129.6.

138 = (1.05) (8) + b

y = m x + b

138 = 8.4 + b

y2 – y1

x2 – x1m =

In most years, the winner of the discus throw was able to throw the discus farther than the previous winner.

Approximating a Best-Fitting Line

230 – 13896 – 8

= 9288

= 1.05

DETERMINING THE CORRELATION OF X AND Y

In this scatter plot, x and y have a positive correlation, which means that the points can be approximated by a line with a positive slope.

DETERMINING THE CORRELATION OF X AND Y

In this scatter plot, x and y have a negative correlation, which means that the points can be approximated by a line with a negative slope.

DETERMINING THE CORRELATION OF X AND Y

In this scatter plot, x and y have relatively no correlation, which means that the points cannot be approximated by a line.

DETERMINING THE CORRELATION OF X AND Y

TYPES OF CORRELATION

Positive Correlation No CorrelationNegative Correlation