# Math Help - How do you find the line of regression?

1. ## How do you find the line of regression?

My teacher said that the "r" estimate is to find the correlation coefficient and that all that the value of "r" tells me is whether or not the relation is strong and if I should construct a rule and then once I confirm that I should, he said to use the midpoint method or something whatever it is called where I take these three coordinates:

1) (1900, 120)
2) (1940, 502)
3) (1990, 1048)

and then I do Δy/Δx with coordinates 3 and 1 above to get the slope of my rule.

I was then told to plug in either 1 or 3 to get the value of b. And then to use the same slope with number 2 then to average the b values out to get the actual one but I keep getting an answer that when I test by plugin in one of the points, is far off.

If it's different in other countries: the equation of a line is y = ax + b.

An example with the rule I've made (y = 10.311111x - 7798.592592) is (to test if my rule is right):

y = 10.311111(1960) - 7798.592592
y = 12411.18518

Clearly, this is wrong.

Can soneome please point out my mistake?

2. $y=ax+b$

with points (1900, 120) & (1990, 1048)

$a = \frac{1048-120}{1990-1900} = \frac{928}{90} = 10.31$

$y=10.31x+b$ use point (1900, 120) to find b

$120=10.31(1900)+b$

$120=19591.1+b$

$b = -19471.1$

is the y intercept way back at x = 0

$y=10.31x-19471.1$

you can re-calculate this regression by making for example the year 1900 your new 0 point giving

1) (0, 120)
2) (40, 502)
3) (90, 1048)

This may be a better domain

3. Your rule seems wrong when I plug in a point and the following seems right not to mention that it was obtained from a graphing calculator that my friend has:

Rule: 10.84220594x-20538.24265