math - Python: Finding a trend in a set of numbers

Question

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?

Answer 1

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