線性迴歸基礎程式碼

# Use linear model to model this data.
from sklearn.linear_model import LinearRegression
import numpy as np

lr=LinearRegression()
lr.fit(pga.distance[:,np.newaxis],pga['accuracy'])  # Another way is using pga[['distance']]
theta0=lr.intercept_
theta1=lr.coef_
print(theta0)
print(theta1)


#calculating cost-function for each theta1
#計算平均累積誤差
def cost(x,y,theta0,theta1):
    J=0
    for i in range(len(x)):
        mse=(x[i]*theta1+theta0-y[i])**2
        J+=mse
    return J/(2*len(x))

theta0=100
theta1s = np.linspace(-3,2,197)
costs=[]
for theta1 in theta1s:
    costs.append(cost(pga['distance'],pga['accuracy'],theta0,theta1))
plt.plot(theta1s,costs)
plt.show()
print(pga.distance)


#調整theta
def partial_cost_theta0(x,y,theta0,theta1):
    #我們的模型是線性擬合函式時：y=theta1*x + theta0，而不是sigmoid函式，當非線性時我們可以用sigmoid
    #直接多整個x series操作，省的一個一個計算，最終求sum 再平均
    h=theta1*x+theta0  
    diff=(h-y)
    partial=diff.sum()/len(diff)
    return partial
partial0=partial_cost_theta0(pga.distance,pga.accuracy,1,1)

def partial_cost_theta1(x,y,theta0,theta1):
    #我們的模型是線性擬合函式：y=theta1*x + theta0，而不是sigmoid函式，當非線性時我們可以用sigmoid
    h=theta1*x+theta0
    diff=(h-y)*x
    partial=diff.sum()/len(diff)
    return partial
partial1=partial_cost_theta1(pga.distance,pga.accuracy,0,5)
print(partial0)
print(partial1)


def gradient_descent(x,y,alpha=0.1,theta0=0,theta1=0):  #設定預設引數
    #計算成本
    #調整權值
    #計算錯誤代價，判斷是否收斂或者達到最大迭代次數
    most_iterations=1000
    convergence_thres=0.000001 
   
    c=cost(x,y,theta0,theta1)
    costs=[c]
    cost_pre=c+convergence_thres+1.0
    
    counter=0
    while( (np.abs(c-cost_pre)>convergence_thres) & (counter<most_iterations) ):
        update0=alpha*partial_cost_theta0(x,y,theta0,theta1)
        update1=alpha*partial_cost_theta1(x,y,theta0,theta1)
        
        theta0-=update0
        theta1-=update1

        cost_pre=c
        c=cost(x,y,theta0,theta1)
        costs.append(c)
        counter+=1
    return  {'theta0': theta0, 'theta1': theta1, "costs": costs}

print("Theta1 =", gradient_descent(pga.distance, pga.accuracy)['theta1'])
costs=gradient_descent(pga.distance,pga.accuracy,alpha=.01)['cost']
print(gradient_descent(pga.distance, pga.accuracy,alpha=.01)['theta1'])
plt.scatter(range(len(costs)),costs)
plt.show()

資料集 ：
複製下面資料，儲存為： pga.csv

distance,accuracy
290.3,59.5
302.1,54.7
287.1,62.4
282.7,65.4
299.1,52.8
300.2,51.1
300.9,58.3
279.5,73.9
287.8,67.6
284.7,67.2
296.7,60
283.3,59.4
284,72.2
292,62.1
282.6,66.5
287.9,60.9
279.2,67.3
291.7,64.8
289.9,58.1
289.8,61.7
298.8,56.4
280.8,60.5
294.9,57.5
287.5,61.8
282.7,56
277.7,72.5
270.5,71.7
285.2,66
315.1,55.2
281.9,67.6
293.3,58.2
286,59.9
285.6,58.2
289.9,65.7
277.5,59
293.6,56.8
301.1,65.4
300.8,63.4
287.4,67.3
281.8,72.6
277.4,63.1
279.1,66.5
287.4,66.4
280.9,62.3
287.8,57.2
261.4,69.2
272.6,69.4
291.3,65.3
294.2,52.8
285.5,49
287.9,61.1
282.2,65.6
301.3,58.2
276.2,61.7
281.6,68.1
275.5,61.2
309.7,53.1
287.7,56.4
291.6,56.9
284.1,65
299.6,57.5
282.7,60
271.5,72
292.1,58.2
295,59.4
274.9,69
273.6,68.7
299.9,60.1
279.9,74
289.9,66
283.6,59.8
310.3,52.4
291.7,65.6
284.2,63.2
295,53.5
298.6,55.1
297.4,60.4
299.7,67.7
284.4,69.7
286.4,72.4
285.9,66.9
297.6,54.3
272.5,62
277,66.2
287.6,60.9
280.4,69.4
280,63.7
295.4,52.8
274.4,68.8
286.5,73.1
287.7,65.2
291.5,65.9
279,69.4
299,65.2
290.1,69.1
288.9,67.9
288.8,68.2
283.2,61
293.2,58.4
285.3,67.3
284.1,65.7
281.4,67.7
286.1,61.4
284.9,62.3
284.8,68.1
296,62
282.9,71.8
280.9,67.8
291.2,62
292.8,62.2
291,61.9
285.7,62.4
283.9,62.9
298.4,61.5
285.1,65.3
286.1,60.1
283.1,65.4
289.4,58.3
284.6,70.7
296.6,62.3
295.9,64.9
295.2,62.8
293.9,54.5
275,65.5
286.8,69.5
291.1,64.4
284.8,62.5
283.7,59.5
295.4,66.9
291.8,62.7
274.9,72.3
302.9,61.2
272.1,80.4
274.9,74.9
296.3,59.4
286.2,58.8
294.2,63.3
284.1,66.5
299.2,62.4
275.4,71
273.2,70.9
281.6,65.9
295.7,55.3
287.1,56.8
287.7,66.9
296.7,53.7
282.2,64.2
291.7,65.6
281.6,73.4
311,56.2
278.6,64.7
288,65.7
276.7,72.1
292,62
286.4,69.9
292.7,65.7
294.2,62.9
278.6,59.6
283.1,69.2
284.1,66
278.6,73.6
291.1,60.4
294.6,59.4
274.3,70.5
274,57.1
283.8,62.7
272.7,66.9
303.2,58.3
282,70.4
281.9,61
287,59.9
293.5,63.8
283.6,56.3
296.9,55.3
290.9,58.2
303,58.1
292.8,61.1
281.1,65
293,61.1
284,66.5
279.8,66.7
292.9,65.4
284,66.9
282,64.5
280.6,64
287.7,63.4
287.7,63.4
298.3,59.5
299.6,53.4
291.3,62.5
295.2,61.4
288,62.4
297.8,59.5
286,62.6
285.3,66.2
286.9,63.4
275.1,73.7