Page 25 - Math SL HB Sem 3

Line of best fit:

To fit the line of best fit by eye:

0 Find and plot the mean point (iJ), where t is the mean of the x-axis data and I is the mean of

the /-axis data.
@ The line of best fit must pass through the mean point (f, i) and lie close to all the other Points - with
approximately an equal number of polnts above and below the line.

\. Example:

ln the example,
circumferences of heads (x)/cm 44.3 48.7 47 .5 45.0 43.1 44.2 48.0 42,6 47 .0
Heights (y)/cm 153 '163 170 165 160 162 164 151 to/

, = 45. 6,7 = 162cone,t b t aecirnat place\

Scatter diagram showing heights against head circumferences
t75 i---+ -ffi
Line of best fit
+
170 1
,1- +- +
165
F r
160
Mean pointj (45.6, 161. 7)
_-r-1-
-1--t
I 155 -f-r
:LT
---
150 --j----
ra
-
l + l-H
145
140 FH
42 43 44 45 46 47 48 49 50
Head cimcumferences /cm

Watch Out:
The line of best fit does not usually pass through the origin!

-4

> Relations to the Pearson's product-moment correlataon coefficient, r:

The closer the data points are to the straight line of best fit, the closer the value of r lies to + 1 or
- 1.

> Relations to the linear regression model:
lf the data set shows at least a moderate positive or negative linear correlation, linear regression
(a straight best-fit line) model can thus be used. Details of linear regression are discussed in the
next chapter.

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