设所求插值函数$f(x)$，是一个$m$次多项式$P_m(x)$

$$ P_m(x)=a_0+a_1x+\cdots+a_mx^m=\sum_{j=0}^ma_jx^j, $$

通过选取多项式的系数$a_j$

$$ \color{red}{\sum_{i=1}^n{\delta_i}^2=\sum_{i=1}^n[y_i-P_m(x_i)]^2=F(a_0,a_1,\cdots,a_m)} $$

使上列式子最小。

def linear_fitting(data_x, data_y):
    size = len(data_x);
    i = 0
    sum_xy = 0
    sum_y = 0
    sum_x = 0
    sum_square_x = 0

    while i < size:
        sum_xy += data_x[i]*data_y[i];
        sum_y += data_y[i]
        sum_x += data_x[i]
        sum_square_x += data_x[i]*data_x[i]
        i += 1

    return_a1 = (size*sum_xy-sum_x*sum_y)/(size*sum_square_x-sum_x*sum_x)
    return_a0 = (sum_y*sum_square_x-sum_x*sum_xy)/(size*sum_square_x-sum_x*sum_x)
    return [return_a1, return_a0]
# 返回多项式的系数这里用来拟合的多项式只有两项