Я пытаюсь установить многомерный набор данных (три независимых переменных, X1, X2, X3 и одна зависимая переменная Y), используя curve_fit, но сейчас я не получаю правильное или самое точное соответствие , r2 (Y and Y_estimated) это просто 0.46, что слишком мало. Я думаю, что это из-за уравнения, которое я использую. Мне нужно иметь какое-то представление о том, какой должна быть формула кривой, чего у меня нет. Итак, что я делал, так это просто настраивал формулу здесь и там, немного пытаясь получить более высокое значение r2.
Прямо сейчас Если я построю Y _estiamted (Y значение, полученное с использованием формулы соответствия) против Y, это выглядит так: 
Мои три независимые переменные и зависимая переменная:
X1=[3.0, 3.0, 3.1, 3.1, 3.2, 3.2, 3.3, 3.3, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.4, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7]
X2=[6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 18.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 24.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0]
X3=[0.0, 9.0, 0.0, 9.0, 0.0, 9.0, 0.0, 9.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 0.0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0]
Y=[-5.890966002, -5.890486683, 2.888846213, -3.87063815, 2.151677659, -2.733484754, 1.472310188, -2.104972457, 0.9167986, -1.728190699, -2.091022903, -6.739492155, 0.877744912, -1.70466657, -2.057078259, -6.427200966, 0.845383533, -1.684086261, -1.923422435, -4.727724352, 0.825849389, -1.67026488, -1.887227147, -4.212293285, 0.820833289, -1.664082205, -1.874008216, -2.431998659, 0.498383392, -1.477976987, -1.77641373, -2.908285403, 0.468936359, -1.464471726, -1.749266847, -3.54492551, 0.443392031, -1.455212292, -1.668808256, -2.886922114, 0.427741259, -1.440518229, -1.648043794, -2.683547022, 0.423972043, -1.438610749, -1.640840076, -1.805421641, 0.20542281, -1.285589215, -1.581456438, -2.214548754, 0.183863714, -1.276677024, -1.565538267, -2.124291602, 0.164031873, -1.268257754, -1.518765332, -1.599120703, 0.151669396, -1.262839985, -1.50499003, -1.559006781, 0.148850528, -1.261237978, -1.500688974, -1.545622269, 0.016590357, -1.120224363, -1.442034612, -1.87137123, -4.670780488, 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len(X1)=len(X2)=len(X3)=len(Y)
И если вы хотите проанализировать файл, чтобы получить данные самостоятельно, вот файл для вас (вы можете открыть файл в новом окне): https://github.com/yanghaobojordan/data/blob/master/results
Первый столбец представляет X1, второй столбец X2, третий столбец X3 и четвертый столбец Y .
Сейчас я использую следующий скрипт:
fitParams, fitCovariances = curve_fit(fitFunc, [X1, X2, X3], Y,maxfev=10000)
print(' fit coefficients:\n', fitParams)
#fit coefficients:
#[0.44560056 1.23433773 -2.98070071 0.02438559 1.03059637]
#calculated Y_estiamted using fit parameters
Y_estimated = [estimate(fitParams, X1[i], X2[i], X3[i]) for i in range(len(X1))]
#plot Y_estiamted vs. Y
fig = plt.figure(num=None, figsize=(9, 7),facecolor='w', edgecolor='k')
ax = fig.add_subplot(111)
ax.scatter(Y, Y_estimated)
lims = [np.min([ax.get_xlim(), ax.get_ylim()]), np.max([ax.get_xlim(), ax.get_ylim()])]
ax.plot(lims, lims, 'k-', alpha=0.75, zorder=0)
ax.set_xlabel('Y',size=15)
ax.set_ylabel('Y_estimated',size=15)
ax.set_aspect('equal')
#compute r2
coeff=R_Square(Y, Y_estimated)
#this is the part which I'm not confident about, I have no idea what the formula should be, so I'm just using my best guess.
def fitFunc(x, a, b, c, d, e):
return a+(b*np.log(x[0]+c))+(d*x[1])+(-np.power(e,x[2]))
def estimate(fit, x1, x2, x3):
return fit[0]+(fit[1]*np.log(x1+fit[2]))+(fit[3]*x2)+(-np.power(fit[4],x3))
def R_Square(x_axis, y_axis):
slope, intercept, r_value, p_value, std_err = stats.linregress(x_axis, y_axis)
return (float(r_value)*float(r_value))
Любая помощь будет принята с благодарностью!