如何在Python中模仿Excel的LOGEST函数

Question

我对用Python模仿Excel的LOGEST函数很感兴趣，但不知道从哪里开始。

Answer 1

这里是使用LOGEST的图形拟合器，如 https://support.office.com/en-us/article/logest-function-f27462d8-3657-4030-866b-a272c1d18b4b

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

xData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.0, 6.6, 7.7])
yData = numpy.array([1.1, 20.2, 30.3, 60.4, 50.0, 60.6, 70.7])

# LOGEST from https://support.office.com/en-us/article/logest-function-f27462d8-3657-4030-866b-a272c1d18b4b
def func(x, b, m):
    y = b * m**x
    return y


# these are the same as the scipy defaults
initialParameters = numpy.array([1.0, 1.0])

# curve fit the test data
fittedParameters, pcov = curve_fit(func, xData, yData, initialParameters)

modelPredictions = func(xData, *fittedParameters) 

absError = modelPredictions - yData

SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))

print('Parameters:', fittedParameters)
print('RMSE:', RMSE)
print('R-squared:', Rsquared)

print()


##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot
    xModel = numpy.linspace(min(xData), max(xData))
    yModel = func(xModel, *fittedParameters)

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot

graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)

Answer 2

您可以使用对数进行线性回归，也可以拟合指数函数。在这里，我展示了分别使用scipy.stats.linregress和scipy.optimize.curve_fit的两种解决方案。

以下是来自Microsoft的Excel中函数LOGEST上documentation的示例：

使用linregress的方法：

from scipy.stats import linregress
import math

x = months = [11, 12, 13, 14, 15, 16]
y = units = [33100, 47300, 69000, 102000, 150000, 220000]

slope, intercept, r_value, p_value, std_err = linregress(
    x,
    list(map(math.log, y)),
    )
print('m', math.exp(slope))
print('b', math.exp(intercept))

输出：

m 1.4632756281161756
b 495.3047701587278

使用curve_fit的方法：

from scipy.optimize import curve_fit

def f(x, b, m):
    return b * m ** x

popt, pcov = curve_fit(f, x, y)
print('m', popt[1])
print('b', popt[0])

输出：

m 1.4678382448967822
b 473.717820465515