之前推導了一元線性回歸和多元線性回歸，今天就用python來實現一下一元線性回歸

先看下之前推導的結果

，

第一種是用循環叠代的計算方法。這裏的x，y是numpy中的array類型

def sum(x):
    sum1 = 0
    for i in x:
        sum1 += i
    return sum1 
def sub(x,y):
    ret = []
    for i in range(len(x)):
        ret.append(x[i] - y)
    return np.array(ret)
def mean(num):
    sum 
 
= 0
    for i in num:
        sum += i
    return sum / len(num)
def multiply(x,y):
    ret = []
    for i in range(len(x)):
        ret.append(x[i]*y[i])
    return np.array(ret)
def square(x):
    ret = []
    for i in range(len(x)):
        ret.append (x[i] * x[i])
    return np.array(ret)
 
def linearRegression(x,y):
    length = len(x)
    t1 = time()
    x_mean1 = mean(x)
    a = sum(multiply(y,sub(x,x_mean1))) / (sum(square(x)) - sum(x) ** 2 / length)
    sum1 = 0
    for i in range(length):
        sum1 += (y[i] - a * x[i])
    b = sum1 / length

第二種人是用vectorization的方法

def
 
 linearRegression_(x,y):
    length = len(x)
    x_mean = x.mean()
    a = (y * (x - x_mean)).sum() / ((x ** 2).sum() - x.sum() ** 2 / length)
    b = (y - a * x).sum() / length

為了比較二者的性能，這裏我們隨機生成10000條數據，分別統計兩種方法運行的時間

x=np.random.randint(0,100,10000)
y=np.random.randint(0,100,10000)

t1 = time() 
linearRegression(x,y)
t2 = time()
print(t2 - t1)

t1 = time()
linearRegression_(x,y)
t2 = time()

得到二者的結果

0.1349632740020752
0.0009996891021728516

上面的是循環計算所需的時間，下面的是vectorization所需得時間。很明顯vectorization要優於循環計算

python實現簡單線性回歸