Fitting A Line To Data
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FITTING A LINE TO DATA 8
There are several ways to find Usually, there is no single line the bestfitting line for a given that passes through all the data set of data points. In this lesson, points, so you try to find the line you will use a graphical that best fits the data. This is bestfitting line. approach. called the bestfitting line.
6 4 2
–8
–6
–4
–2
0 –2 –4 –6 –8
2
4
6
Approximating a BestFitting 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 bestfitting line for these throws.
240
190 180 170 160 150 140 130 120 110 100
0
8
16
24
32
40
48
56
64
72
Years since 1900
80
88
96
104
Approximating a BestFitting Line 250
SOLUTION
Find the slope of the line through these points.
230 220 210 200
Distance (ft)
Find two points that lie on the bestfitting line, such as (8, 138) and (96, 230))..
(96, 230)
240
190 180 170 160 150 140
(8, 138)
130 120 110 100
0
8
16
24
32
40
48
56
64
72
Years since 1900
80
88
96
104
Approximating a BestFitting Line 250
y2 – y1 – 138230= 92 1.05 m = x – x = 230 96 – 8 220 88 2 1 240
y = m=x 8.4 + + b b 138
129.6 = b
Distance (ft)
– 138 = y230 = m x + b 96 – 8 = 92 138 1.05 (8) + b 88= (1.05)
210 200 190 180 170 160 150 140 130
(96, 230)
Write slope intercept form. Substitute 1.05 for
138 for y.
m, 8 for x,
Simplify.
b
Solve for . (8, 138)
An equation of the bestfitting line is y = 1.05 x + 129.6. 120 110
100 In most years, the winner of the discus throw was able to 0 8 16 24 32 40 48 56 64 72 80 throw the discus farther than the 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
There are several ways to find Usually, there is no single line the bestfitting line for a given that passes through all the data set of data points. In this lesson, points, so you try to find the line you will use a graphical that best fits the data. This is bestfitting line. approach. called the bestfitting line.
6 4 2
–8
–6
–4
–2
0 –2 –4 –6 –8
2
4
6
Approximating a BestFitting 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 bestfitting line for these throws.
240
190 180 170 160 150 140 130 120 110 100
0
8
16
24
32
40
48
56
64
72
Years since 1900
80
88
96
104
Approximating a BestFitting Line 250
SOLUTION
Find the slope of the line through these points.
230 220 210 200
Distance (ft)
Find two points that lie on the bestfitting line, such as (8, 138) and (96, 230))..
(96, 230)
240
190 180 170 160 150 140
(8, 138)
130 120 110 100
0
8
16
24
32
40
48
56
64
72
Years since 1900
80
88
96
104
Approximating a BestFitting Line 250
y2 – y1 – 138230= 92 1.05 m = x – x = 230 96 – 8 220 88 2 1 240
y = m=x 8.4 + + b b 138
129.6 = b
Distance (ft)
– 138 = y230 = m x + b 96 – 8 = 92 138 1.05 (8) + b 88= (1.05)
210 200 190 180 170 160 150 140 130
(96, 230)
Write slope intercept form. Substitute 1.05 for
138 for y.
m, 8 for x,
Simplify.
b
Solve for . (8, 138)
An equation of the bestfitting line is y = 1.05 x + 129.6. 120 110
100 In most years, the winner of the discus throw was able to 0 8 16 24 32 40 48 56 64 72 80 throw the discus farther than the 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
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