POLYNOMIAL REGRESSION 中文是什么意思 - 中文翻译

• 多项式回归

在 英语 中使用 Polynomial regression 的示例及其翻译为 中文

Polynomial Regression.
项回归.

Import numpy and matplotlib then draw the line of Polynomial Regression:.
导入numpy和matplotlib再画多项式回归的路线：.

Polynomial regression: extending linear models with basis functions.
多项式回归：基函数扩展线性模型.

Some of these methods make use of a localized form of classical polynomial regression.
这些方法中的一些利用了经典多项式回归的局部形式。

A single object representing a simple polynomial regression can be created and used as follows:.
可以创建表示简单多项式回归的单个对象，并使用如下：.

These values for the x- and y-axis should result in a very bad fit for polynomial regression:.
X和y轴的这些值将导致多项式回归的拟合度非常差：.

The vector of estimated polynomial regression coefficients(using ordinary least squares estimation) is.
估计多项式回归系数的向量（使用最小二乘估计）为.

Most of them are scalable to more generalized multi-variate and polynomial regression modeling too.
大多数都可以扩展到更一般化的多元和多项式回归建模中。

Let us create an example where polynomial regression would not be the best method to predict future values.
让我们创建一个示例，其中多项式回归不是预测未来值的最佳方法。

If the power of the independent variable(X) is more than 1, then it's known as polynomial regression.
如果自变量（X）的幂大于1，那么它被称为多项式回归。

The first design of an experiment for polynomial regression appeared in an 1815 paper of Gergonne.
多项式回归实验的第一个设计出现在1815年的Gergonne的论文中。

Python has methods for finding a relationship between data-points and to draw a line of polynomial regression.
Python有一些方法可以找到数据点之间的关系并画出多项式回归线。

For this reason, polynomial regression is considered to be a special case of multiple linear regression..
因此，多项式回归被认为是多元线性回归的特例。

Most of them are scalable to more generalized multi-variate and polynomial regression modeling too.
它们中的大多数都可以扩展到更一般化的多变量和多项式回归建模。

Returning to the polynomial regression problem, we can plot the model evidence against the order of the polynomial, as shown in Figure 3.14.
回到多项式回归问题，我们可以画出模型证据与多项式阶数之间的关系，如图3.14所示。

They usually can achieve pretty high performance, better than polynomial regression and often on par with neural networks.
通常可以实现相当高的性能，优于多项式回归，并且性能通常与神经网络相当。

Therefore, non-parametric regression approaches such as smoothing can be useful alternatives to polynomial regression.
因此，诸如平滑的非参数回归方法可以是多项式回归的有效替代方案。

As an improvement over this model, I tried Polynomial Regression which generated better results(most of the time).
为了改进这个问题模型，我尝试了多项式回归，效果确实好一些（大多数情况下都是如此会改善）。

The result: 0.00995 indicates a very bad relationship, and tells us that this data set is not suitable for polynomial regression.
结果：0.00995表示关系很差，并告诉我们该数据集不适合多项式回归。

A cubic polynomial regression fit to a simulated data set. The confidence band is a 95% simultaneous confidence band constructed using the Scheffé approach.
三次多项式回归拟合模拟数据集。置信区间是使用Scheffé方法构建的95％置信区间。

Note: The result 0.94 shows that there is a very good relationship, and we can use polynomial regression in future predictions.
注意：结果0.94表明存在很好的关系，我们可以在将来的预测中使用多项式回归。

In the twentieth century, polynomial regression played an important role in the development of regression analysis, with a greater emphasis on issues of design and inference.
在二十世纪，多项式回归在回归分析的发展中起着重要作用，更加强调设计和推理的问题。

In general, we can model the expected value of y as an nth degree polynomial, yielding the general polynomial regression model.
通常，我们可以将y的期望值建模为n次多项式，得到一般多项式回归模型：.

By traditional ML, we are referring to techniques such as polynomial regression, kernel density methods, and state-space estimation methods(e.g. Kalman filters).
通过传统的ML，我们指的是诸如多项式回归，核密度方法和状态空间估计方法（例如卡尔曼滤波器）之类的技术。

Another example of a model representing i. i. d. data is the graph in Figure 8.7 corresponding to Bayesian polynomial regression.
另一个表示独立同分布数据模型的例子如图8.7所示，它对应于贝叶斯多项式回归。

Curve fitting Line regression Local polynomial regression Polynomial and rational function modeling Polynomial interpolation Response surface methodology Smoothing spline.
曲线拟合线性回归局部多项式回归多项式和有理函数建模多项式差值反应曲面法平滑样条曲线.

If your data points clearly will not fit a linear regression(a straight line through all data points), it might be ideal for polynomial regression.
如果您的数据点显然不适合线性回归（所有数据点之间的直线），则可能是多项式回归的理想选择。

An advantage of traditional polynomial regression is that the inferential framework of multiple regression can be used(this also holds when using other families of basis functions such as splines).
传统多项式回归的一个优点是可以使用多元回归的推理框架（当使用其他基函数族，如样条函数时也是如此）。

Although polynomial regression is technically a special case of multiple linear regression, the interpretation of a fitted polynomial regression model requires a somewhat different perspective.
虽然多项式回归在技术上是多元线性回归的一个特例，但拟合多项式回归模型的解释需要一个不同的视角。

The goal of polynomial regression is to model a non-linear relationship between the independent and dependent variables(technically, between the independent variable and the conditional mean of the dependent variable).
多项式回归的目标是模拟独立变量和因变量之间的非线性关系（在自变量和因变量的条件均值之间）。