SOLUTION: This is a homework question. I do not understand about regression lines. The question is: Find the equation of the regression line: x 12 14 10 9 15 8 __

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Question 159471: This is a homework question. I do not understand about regression lines.
The question is: Find the equation of the regression line:
x 12 14 10 9 15 8
____________________________________
y 29 35 28 23 36 18
Multiple choice answer:
y = -1.2 + 2.4x
y = 1.2 + 2.4x
y = 2.4 + 1.2x
y = -2.4 + 1.2x
Which is the correct answer?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A regression line is the best fit of a straight line using the data points.
It doesn't necessarily go through all or any of the points but fits the data best (least error at each of the data points).
A regression analysis uses the data to find the slope, m, of the line, and the y-intercept, b.
y=mx%2Bb
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.
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Let's see if we can guess the solution without doing a full blown regression analysis.
I'm not sure if that was the intent of the problem.
First look at the data,

You can guess the approximate slope by using the first and last points,
m%5Bapx%5D=%2836-18%29%2F%2815-8%29=2.57
So the answer must be 2.4, closer to 2.4 than 1.2.
You know that b=y%5Bave%5D-mx%5Bave%5D
x%5Bave%5D=%2812%2B14%2B10%2B9%2B15%2B9%29%2F6=11.333
x%5Bave%5D=%2829%2B35%2B28%2B23%2B36%2B18%29%2F6=28.167
b=y%5Bave%5D-mx%5Bave%5D
b=28.167-%282.4%29%2811.333%29
b=28.167-27.2
b=0.97
The closest answer is 1.2.
y=1.2%2B2.4x
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.
.
The value for b was off because of roundoff error in m.
The actual calculated value for m=2.3814, with b=1.178.