y = 813402593.2415 + 1.0527x1 + 7.8389x2 + -6.4792x3 + -5638.5189x4 + 0.34774x5 + 3.5502x6,对此方程绘制多元回归曲线,用matlab实现
时间: 2023-06-28 10:05:29 浏览: 261
首先,我们需要导入数据并拟合多元线性回归模型。假设我们的数据文件名为“data.csv”,包含6列自变量和1列因变量:
```matlab
% 导入数据
data = readmatrix('data.csv');
% 分离自变量和因变量
x = data(:,1:6);
y = data(:,7);
% 拟合多元线性回归模型
mdl = fitlm(x,y);
```
接下来,我们可以使用`meshgrid`函数生成平面上的网格点,并计算每个点的预测值。然后,使用`surf`函数绘制回归曲面:
```matlab
% 生成网格点
[x1,x2] = meshgrid(min(x(:,1)):100:max(x(:,1)), min(x(:,2)):100:max(x(:,2)));
[n1,n2] = size(x1);
x3 = ones(n1, n2) * mean(x(:,3));
x4 = ones(n1, n2) * mean(x(:,4));
x5 = ones(n1, n2) * mean(x(:,5));
x6 = ones(n1, n2) * mean(x(:,6));
X = [x1(:), x2(:), x3(:), x4(:), x5(:), x6(:)];
% 计算预测值
Y = predict(mdl, X);
% 绘制回归曲面
surf(x1,x2,reshape(Y,n1,n2));
xlabel('x1');
ylabel('x2');
zlabel('y');
```
这样,就可以得到多元回归曲面的可视化结果了。完整的代码如下:
```matlab
% 导入数据
data = readmatrix('data.csv');
% 分离自变量和因变量
x = data(:,1:6);
y = data(:,7);
% 拟合多元线性回归模型
mdl = fitlm(x,y);
% 生成网格点
[x1,x2] = meshgrid(min(x(:,1)):100:max(x(:,1)), min(x(:,2)):100:max(x(:,2)));
[n1,n2] = size(x1);
x3 = ones(n1, n2) * mean(x(:,3));
x4 = ones(n1, n2) * mean(x(:,4));
x5 = ones(n1, n2) * mean(x(:,5));
x6 = ones(n1, n2) * mean(x(:,6));
X = [x1(:), x2(:), x3(:), x4(:), x5(:), x6(:)];
% 计算预测值
Y = predict(mdl, X);
% 绘制回归曲面
surf(x1,x2,reshape(Y,n1,n2));
xlabel('x1');
ylabel('x2');
zlabel('y');
```
需要注意的是,该方法只适用于自变量为2~3个的情况。如果自变量更多,可以考虑使用主成分回归或LASSO回归等方法来降低自变量的维度。
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