Transcript Approximating a Best

FITTING A LINE TO DATA
8
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called the best-fitting
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Approximating a Best-Fitting Line
250
DISCUS THROWS
Write an equation of
your line.
230
220
210
200
Distance (ft)
The winning Olympic
discus throws from 1908
to 1996 are plotted in
the graph. Approximate
the best-fitting line for
these throws.
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190
180
170
160
150
140
130
120
110
100
0
8
16
24
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40
48
56
64
72
Years since 1900
80
88
96
104
Approximating a Best-Fitting Line
250
SOLUTION
Find the slope of the line
through these points.
(96, 230)
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220
210
200
Distance (ft)
Find two points that lie
on the best-fitting line,
such as (8, 138) and
(96, 230))..
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190
180
170
160
150
140
(8, 138)
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110
100
0
8
16
24
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40
48
56
64
72
Years since 1900
80
88
96
104
Approximating a Best-Fitting Line
250
y2 – y1 230 – 138
m = x – x = 96 – 8 230= 92
88
2
1
220
240
y138
= mx
+ b+ b
= 8.4
Distance (ft)
– 138
= y230
=
mx
96 – 8 + b
138
= (1.05)
= 92
1.05(8) + b
88
1.05
(96, 230)
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200
190
180
Write slope intercept form.
Substitute 1.05 for m, 8 for x,
138 for y.
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160
Simplify.
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129.6 = b
140
130
Solve for b.
(8, 138)
An equation of the best-fitting line is y = 1.05 x + 129.6.
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110
In most years, the winner of
100 the discus throw was able to
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24
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40
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throw the discus farther than 0the8 previous
winner.
Years since 1900
88
96
104
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
Negative Correlation
No Correlation