# Python: Finding a trend in a set of numbers

mathpython

I have a list of numbers in Python, like this:

``````x = [12, 34, 29, 38, 34, 51, 29, 34, 47, 34, 55, 94, 68, 81]
``````

What's the best way to find the trend in these numbers? I'm not interested in predicting what the next number will be, I just want to output the trend for many sets of numbers so that I can compare the trends.

Edit: By trend, I mean that I'd like a numerical representation of whether the numbers are increasing or decreasing and at what rate. I'm not massively mathematical, so there's probably a proper name for this!

Edit 2: It looks like what I really want is the co-efficient of the linear best fit. What's the best way to get this in Python?

#### Best Solution

Possibly you mean you want to plot these numbers on a graph and find a straight line through them where the overall distance between the line and the numbers is minimized? This is called a linear regression

``````def linreg(X, Y):
"""
return a,b in solution to y = ax + b such that root mean square distance between trend line and original points is minimized
"""
N = len(X)
Sx = Sy = Sxx = Syy = Sxy = 0.0
for x, y in zip(X, Y):
Sx = Sx + x
Sy = Sy + y
Sxx = Sxx + x*x
Syy = Syy + y*y
Sxy = Sxy + x*y
det = Sxx * N - Sx * Sx
return (Sxy * N - Sy * Sx)/det, (Sxx * Sy - Sx * Sxy)/det

x = [12, 34, 29, 38, 34, 51, 29, 34, 47, 34, 55, 94, 68, 81]
a,b = linreg(range(len(x)),x)  //your x,y are switched from standard notation
``````

The trend line is unlikely to pass through your original points, but it will be as close as possible to the original points that a straight line can get. Using the gradient and intercept values of this trend line (a,b) you will be able to extrapolate the line past the end of the array:

``````extrapolatedtrendline=[a*index + b for index in range(20)] //replace 20 with desired trend length
``````