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copied!<p>You can also use numpy's <a href="http://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html" rel="noreferrer">polyfit</a>:</p> <pre><code>data = np.array([[1,5], [2,10], [3,15], [4,20], [5,25]]) fit = np.polyfit(data[:,0], data[:,1] ,1) #The use of 1 signifies a linear fit. fit [ 5.00000000e+00 1.58882186e-15] #y = 5x + 0 line = np.poly1d(fit) new_points = np.arange(5)+6 new_points [ 6, 7, 8, 9, 10] line(new_points) [ 30. 35. 40. 45. 50.] </code></pre> <p>This allows you to alter the degree of the polynomial fit quite easily as the function <code>polyfit</code> take thes following arguments <code>np.polyfit(x data, y data, degree)</code>. Shown is a linear fit where the returned array looks like <code>fit[0]*x^n + fit[1]*x^(n-1) + ... + fit[n-1]*x^0</code> for any degree <code>n</code>. The <code>poly1d</code> function allows you turn this array into a function that returns the value of the polynomial at any given value <code>x</code>.</p> <p>In general extrapolation without a well understood model will have sporadic results at best.</p> <hr> <p>Exponential <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html" rel="noreferrer">curve fitting</a>.</p> <pre><code>from scipy.optimize import curve_fit def func(x, a, b, c): return a * np.exp(-b * x) + c x = np.linspace(0,4,5) y = func(x, 2.5, 1.3, 0.5) yn = y + 0.2*np.random.normal(size=len(x)) fit ,cov = curve_fit(func, x, yn) fit [ 2.67217435 1.21470107 0.52942728] #Variables y [ 3. 1.18132948 0.68568395 0.55060478 0.51379141] #Original data func(x,*fit) [ 3.20160163 1.32252521 0.76481773 0.59929086 0.5501627 ] #Fit to original + noise </code></pre>

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