A nice easy linear expression question for you (or is it?)

[Psycho_NZ]

Hiya, i have a database full of records and each has 4 points. i want to take these four points, and plot a line of best fit for them without having to draw the graph for them (cause i want to make my program do it you see). So.. how can you, given four not exactly straight line points, obtain an approxiamte linear equation for them?


Thanks for you time
Ang

[sql_lall]

Not exactly sure, but it has something to do with the sum of the squares of the differences between the points and the line.
Kinda like Chi-squared

[wy125]

Psycho_NZ

What you want to do is called regression. You're trying to choose a slope and intercept that give you the smallest differences between the fitted line and your data points (least-squares).

Anyway, here are the formulas:

The slope of the best-fit line, m, is given by

m = [nSum(xy) - Sum(x)Sum(y)]/[nSum(x^2) - (Sum(x))^2]


where
n is the number of data points

and

Sum(x) is the sum of all your x values
Sum(xy) is the sum of the product of each x and y pair
and so on...

The intercept, b, is given by


b = Yavg - mXavg

where

Yavg = the average of all Y values
Xavg = the average of all X values


That will give you the best fit line.

[Psycho_NZ]

Hey your notation is way easier to understand than the websites i found on it.

Thanks
Ang