Fit a polynomial of degree 1–5 to (x, y) points by least squares: normal equations solved with partial-pivot Gaussian elimination, reported as the fitted equation, R², RMSE and per-degree coefficients.
Degree 1 is plain linear regression (same answers as the Descriptive Statistics tool); higher degrees trade extrapolation safety for local fit — watch RMSE, not just R², before believing a degree-5 curve through 6 points.
Frequently asked questions
Why does it refuse to fit sometimes?
The normal equations become singular when there are not enough distinct x values (or fewer points than coefficients) — the message says so instead of returning garbage coefficients.
Should I always pick the highest degree?
No. A degree-5 polynomial through 6 points has zero residual and zero predictive value. Prefer the lowest degree whose RMSE stops improving meaningfully.
中文说明
对 (x, y) 数据点做 1–5 次多项式最小二乘拟合：正规方程经列主元高斯消元求解，输出拟合方程、R²、RMSE 与各次系数。
1 次即普通线性回归（与描述统计工具同答案）；更高次数用外推安全性换局部拟合——相信一条穿过 6 个点的 5 次曲线之前，先看 RMSE 而不只是 R²。
常见问题
为什么有时拒绝拟合？
当 x 取值不够分散（或点数少于系数个数）时正规方程奇异——工具会如实提示，而不是给出垃圾系数。
次数越高越好吗？
不是。穿过 6 个点的 5 次多项式残差为零、预测价值也为零。选 RMSE 不再明显下降的最低次数。