In python, how to fit linear slope to a graph in a specified range of x values? -

for example, here data set:

x: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

y: 20, 21, 22, 26, 32, 41, 39, 36, 29, 23

i think i'm supposed using numpy polyfit function, not sure. how can i, example, linear fit between x(3) , x(6)?

just calculating in head, should like: rise/run = (41-22)/(6-3) = 6.3333333...

i'm dealing different data sets each time read in .txt files, appreciate if showed me general method this, apply future datasets.

i assume want least square fit, polyfit give you.

to achieve that, pass 2 lists polyfit, x values, y values , have set order of polynomial want. example, turn out be

import numpy np  x = [3, 6] y = [22, 41] coeffs = np.polyfit(x, y, 1)  # y values of resulting line x = np.arange(1,11) y_line = x * coeffs[0] + coeffs[1] 

with regard further questions, need think output of polyfit.

the documentation numpy.polyfit says

the solution minimizes squared error

e = \sum_{j=0}^k |p(x_j) - y_j|^2

in equations:

x[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0]

x1**n * p[0] + ... + x1 * p[n-1] + p[n] = y1

...

x[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k]

we using simplified case, because straight line, have polynomial of first order, is, n=1.

that means in our case, equation y y[k] = x[k]*p[0]+p[1]. compare general form of line equation y = k*x+d. see slope of line coeffs[0].

as plotting, see following example

import numpy np matplotlib import pyplot plt  x = np.arange(1, 11) y = [20, 21, 22, 26, 32, 41, 39, 36, 29, 23]  poly = np.polyfit(x, y, 1)  y_line = x * poly[0] + poly[1]  print poly[0]  plt.scatter(x, y) plt.plot(x, y_line) plt.show() 

which results in output

$ python test.py  1.21818181818