x=[0.5,1,1.5,2,2.5,3,3.5,4,4.5,5];%自变量
y=[191,321,442,565,686,819,930,1032,1153,1252];%因变量
xmean=mean(x);ymean=mean(y);
sumx2=(x-xmean)*(x-xmean)';
sumxy=(y-ymean)*(x-xmean)';
a=sumxy/sumx2;%解出直线斜率a(即传感器灵敏度) b=ymean-a*xmean;%解出直线截距b
z=((a*(x(1,10))+b-(y(1,10)))/(y(1,10)));%“10”是自变量的个数,z为非线性误差(即线性度)
a
b
z
拟合直线figure
plot(x,y,'+');
hold on
% 用红绘制拟合出的直线
px=linspace(0,6,50);%(linspace语法(从横坐标负轴起点0画到横坐标正轴终点6,50等分精度)) py=a*px+b;
plot(px,py,'r');
运行结果:
a =236.9818 b =87.4000
另一种简单一点的方法:
%最小二乘法线性拟合y=ax+b
x=[0.5,1,1.5,2,2.5,3,3.5,4,4.5,5];%自变量
y=[191,321,442,565,686,819,930,1032,1153,1252];%因变量
p=polyfit(x,y,1);
p
运行结果:
p =
236.9818 87.4000