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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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8
6
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0 2 4 6–2–4–6–8
FITTING A LINE TO DATALesson 5.4
Approximating a Best-Fitting Line
DISCUS THROWS
Years since 1900
Dis
tanc
e (f
t)
0 8 16 24 32 40 48 56 64 72 80 88 96 104100
110
120
130
140
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180
190
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230
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250
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
Years since 1900
Dis
tanc
e (f
t)
0 8 16 24 32 40 48 56 64 72 80 88 96 104100
110
120
130
140
150
160
170
180
190
200
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230
240
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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
Years since 1900
Dis
tanc
e (f
t)
0 8 16 24 32 40 48 56 64 72 80 88 96 104100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
(96, 230)
(8, 138)
y = m x + b
230 – 13896 – 8
=
129.6 = b
Write slope intercept form.
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
Approximating a Best-Fitting Line
DETERMINING THE CORRELATION OF X AND Y
In this scatter plot, x and y have a positive correlation,
positive slope.
DETERMINING THE CORRELATION OF X AND Y
In this scatter plot, x and y have a negative correlation,
negative slope.
DETERMINING THE CORRELATION OF X AND Y
In this scatter plot, x and y have relatively no correlation,
DETERMINING THE CORRELATION OF X AND Y
TYPES OF CORRELATION
Positive Correlation No CorrelationNegative Correlation
