1. FITTING A LINE TO DATA –8 8 6 4 2 –2 –4 –6
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.
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.

2. Write an equation of your line.
Approximating a Best-Fitting Line
Years since 1900
Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96
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DISCUS THROWS
The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws.
Write an equation of your line.

3. Approximating a Best-Fitting Line
Years since 1900
Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96
104
100
110
120
130
140
150
160
170
180
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220
230
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SOLUTION
(96, 230).
(96, 230)
Find two points that lie on the best-fitting line, such as (8, 138) and (96, 230).
(8, 138)
Find the slope of the line through these points.

4. m = y = m x + b y = m x + b 138 = (1.05) (8) + b 138 for y.
Approximating a Best-Fitting Line
Years since 1900
Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96
104
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
(96, 230)
(8, 138)
y2 – y1
x2 – x1
m =
230 – 138
96 – 8 = 92 88
1.05
230 – 138
96 – 8 =
y = m x + b
Write slope intercept form.
Substitute 1.05 for m, 8 for x,
138 for y.
138 = (1.05) (8) + b 92 88 =
1.05
y = m x + b
138 = b
Simplify.
= b
Solve for b.
An equation of the best-fitting line is y = 1.05 x
In most years, the winner of the discus throw was able to throw the discus farther than the previous winner.

5. 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.

6. 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.

7. 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.

8. DETERMINING THE CORRELATION OF X AND Y
TYPES OF CORRELATION
Positive Correlation
Negative Correlation
No Correlation