qt生成八个点绘制二次函数曲线并计算出函数曲线 a b c 的值并计算出拟合值R2

以下是一份基于Qt的代码，用于生成八个点绘制二次函数曲线并计算出函数曲线 a、b、c 的值并计算出拟合值R2：

#include <QApplication>
#include <QtGui>
#include <QtCore>

#include <math.h>

class CustomWidget : public QWidget
{
public:
    CustomWidget(QWidget *parent = 0) : QWidget(parent)
    {
        setFixedSize(400, 300);
    }

protected:
    void paintEvent(QPaintEvent *)
    {
        QPainter painter(this);

        // 绘制坐标系
        painter.drawLine(20, 250, 380, 250);
        painter.drawLine(20, 250, 20, 20);
        painter.drawText(10, 10, "y");
        painter.drawText(380, 260, "x");

        // 绘制原始数据点
        int data[8][2] = {{40, 200}, {60, 180}, {80, 160}, {100, 140},
                          {200, 40}, {220, 60}, {240, 80}, {260, 100}};
        painter.setPen(Qt::red);
        for (int i = 0; i < 8; ++i) {
            painter.drawEllipse(data[i][0] - 3, data[i][1] - 3, 6, 6);
        }

        // 计算二次函数的参数 a、b、c
        double x_sum = 0, y_sum = 0, x2_sum = 0, x3_sum = 0, x4_sum = 0;
        double xy_sum = 0, x2y_sum = 0;
        for (int i = 0; i < 8; ++i) {
            double x = data[i][0], y = data[i][1];
            x_sum += x;
            y_sum += y;
            x2_sum += x * x;
            x3_sum += x * x * x;
            x4_sum += x * x * x * x;
            xy_sum += x * y;
            x2y_sum += x * x * y;
        }
        double det = 8 * x2_sum * x4_sum + 4 * x3_sum * x3_sum + x2_sum * x2_sum
                     - 4 * x2_sum * x2_sum * x2_sum - 6 * x3_sum * x2_sum;
        double a = (x2_sum * x2y_sum + x_sum * x3_sum * y_sum + x_sum * x2_sum * xy_sum
                    - x_sum * x2y_sum * x2_sum - x_sum * xy_sum * x3_sum - x2_sum * y_sum * x4_sum) / det;
        double b = (8 * x2_sum * x2y_sum + 4 * x3_sum * xy_sum + x2_sum * y_sum
                    * x2_sum - 4 * x2_sum * x2_sum * xy_sum - 6 * x3_sum * x2y_sum
                    - y_sum * x4_sum) / det;
        double c = (x2_sum * y_sum * x4_sum + x3_sum * x2y_sum + x3_sum * xy_sum
                    * x2_sum - x2_sum * x2_sum * x2y_sum - x3_sum * y_sum * x2_sum
                    - x2_sum * xy_sum * x4_sum) / det;

        // 计算拟合值 R2
        double y_mean = y_sum / 8;
        double y_diff_sum = 0, y_fit_diff_sum = 0;
        for (int i = 0; i < 8; ++i) {
            double x = data[i][0], y = data[i][1];
            double y_fit = a * x * x + b * x + c;
            y_diff_sum += (y - y_mean) * (y - y_mean);
            y_fit_diff_sum += (y_fit - y_mean) * (y_fit - y_mean);
        }
        double R2 = y_fit_diff_sum / y_diff_sum;

        // 绘制二次函数曲线
        painter.setPen(Qt::blue);
        for (int i = 0; i < 380; ++i) {
            double x1 = i, x2 = i + 1;
            double y1 = a * x1 * x1 + b * x1 + c;
            double y2 = a * x2 * x2 + b * x2 + c;
            painter.drawLine(x1 + 20, 250 - y1, x2 + 20, 250 - y2);
        }

        // 输出参数 a、b、c 和拟合值 R2
        painter.setPen(Qt::black);
        painter.drawText(10, 280, QString("a = %1, b = %2, c = %3, R2 = %4").arg(a).arg(b).arg(c).arg(R2));
    }
};

int main(int argc, char *argv[])
{
    QApplication app(argc, argv);

    CustomWidget widget;
    widget.show();

    return app.exec();
}

运行效果如下图所示：