Question 672408
x|y
2|1
4|3
5|5
7|6
3|18
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Line that include data points, chose (2,1) and (7,6) from visual quick plot of the points.
slope = {{{(1-6)/(2-7) = -5/-5 = 1}}}
y - 1 = 1(x-2)
y = x - 2 + 1
{{{highlight_green(y = x-1)}}}
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Line that does not include the data points
Using the "least square method" for best fit line
Find xy and x^2
x|y|xy|x^2
2|1|2|4
4|3|12|16
5|5|25|25
7|6|42|49
3|18|54|9
..........
21|33|135|103  ==> Sums of each column
...
slope = {{{(135-((21*33)/5))/(103-(21^2/5))}}}
= {{{(135-(693/5))/(103-(441/5)))}}}
= {{{-3.6 / 14.8 = -.243}}}
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y-intercept
6.6 - 4.2(-.243) = 7.62
...
Best fit line
{{{highlight(y = -.243x + 7.62)}}}
...
For an explanation of the forumula
http://hotmath.com/hotmath_help/topics/line-of-best-fit.html
...
The first equation is a better model, as there are only two outliers from the line, one more extreme than the other.  This line thereby captures on it three of the 5 data points.  The second line, while a true "best fit line" captures none of the data points and represents too wide of a variance resulting from one extreme outlier.  Not to mention the negative slope, whereas, the data represents a positive slope trend, not a negative one.
...
{{{graph(300,200,-10,10,-10,10,-.243x+7.62,x-1)}}}

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