Fitting toolbox error parameter

Fitting toolbox error parameters

Invisible city Released | October 22, 2018| machine learning , technology |5979 Browse

<trans data-src="使用过Matlab的拟合、优化和统计等工具箱的网友，会经常遇到下面几个名词：">Netizens who have used Matlab's fitting, optimization and statistics toolkits will often encounter the following terms:</trans> <trans data-src="SSE(和方差、误差平方和)：The sum of squares due to error">SSE (sum of squares due to error): The sum of squares due to error</trans> <trans data-src="MSE(均方差、方差)：Mean squared error">MSE: Mean squared error</trans> <trans data-src="RMSE(均方根、标准差)：Root mean squared error">RMSE (root mean square error):</trans> <trans data-src="R-square(确定系数)：Coefficient of determination">R-square: Coefficient of determination</trans> <trans data-src="Adjusted R-square：Degree-of-freedom adjusted coefficient of determination">Adjusted R-square：Degree-of-freedom adjusted coefficient of determination</trans> <trans data-src="下面我对以上几个名词进行详细的解释下，相信能给大家带来一定的帮助！！">Now I will explain the above terms in detail, and I believe it will help you!!</trans> <trans data-src="一、SSE(和方差)">1、 SSE (and variance)</trans> <trans data-src="该统计参数计算的是拟合数据和原始数据对应点的误差的平方和，计算公式如下">This statistical parameter calculates the square sum of the errors of the corresponding points of the fitting data and the original data, and the calculation formula is as follows</trans> <trans data-src="SSE,MSE,RMSE,R-square(转)">SSE, MSE, RMSE, R-square (turn)</trans> <trans data-src="SSE越接近于0，说明模型选择和拟合更好，数据预测也越成功。">The closer the SSE is to 0, the better the model selection and fitting are, and the more successful the data prediction is.</trans> <trans data-src="接下来的MSE和RMSE因为和SSE是同出一宗，所以效果一样">The following MSE and RMSE have the same effect as SSE</trans> <trans data-src="二、MSE(均方差)">2、 MSE</trans> <trans data-src="该统计参数是预测数据和原始数据对应点误差的平方和的均值，也就是SSE/n，和SSE没有太大的区别，计算公式如下">The statistical parameter is the mean value of the sum of squares of the corresponding point errors of the predicted data and the original data, that is SSE/n. It is not very different from SSE. The calculation formula is as follows</trans> <trans data-src="mse.gif">mse.gif</trans> <trans data-src="三、RMSE(均方根)">3、 RMSE</trans> <trans data-src="该统计参数，也叫回归系统的拟合标准差，是MSE的平方根，就算公式如下">The statistical parameter, also called the fitting standard deviation of the regression system, is the square root of MSE, and the formula is as follows</trans> <trans data-src="rmse.gif">rmse.gif</trans> <trans data-src="在这之前，我们所有的误差参数都是基于预测值(y_hat)和原始值(y)之间的误差(即点对点)。">Before that, all our error parameters were based on the error between the predicted value (y_hat) and the original value (y) (that is, point-to-point).</trans> <trans data-src="从下面开始是所有的误差都是相对原始数据平均值(y_ba)而展开的(即点对全)!!!">From the following, all errors are expanded relative to the average value of the original data (y_ba) (that is, point to all)!!!</trans> <trans data-src="四、R-square(确定系数)">4、 R-square (determination coefficient)</trans> <trans data-src="在讲确定系数之前，我们需要介绍另外两个参数SSR和SST，因为确定系数就是由它们两个决定的">Before we talk about the determination coefficient, we need to introduce the other two parameters, SSR and SST, because the determination coefficient is determined by them</trans> <trans data-src="(1)SSR：Sum of squares of the regression，即预测数据与原始数据均值之差的平方和，公式如下">(1) SSR: Sum of squares of the region, that is, the sum of squares of the difference between the mean value of the predicted data and the original data. The formula is as follows</trans> <trans data-src="ssr.gif">ssr.gif</trans> <trans data-src="(2)SST：Total sum of squares，即原始数据和均值之差的平方和，公式如下">(2) SST: Total sum of squares, that is, the sum of squares of the difference between the original data and the mean value. The formula is as follows</trans> <trans data-src="sst.gif">sst.gif</trans> <trans data-src="细心的网友会发现，SST=SSE+SSR，呵呵只是一个有趣的问题。">Careful netizens will find that SST=SSE+SSR is just an interesting question.</trans> <trans data-src="而我们的“确定系数”是定义为SSR和SST的比值，故">Our "determination coefficient" is defined as the ratio of SSR and SST, so</trans> <trans data-src="rsquare.gif">rsquare.gif</trans> <trans data-src="其实“确定系数”是通过数据的变化来表征一个拟合的好坏。">In fact, the "determination coefficient" is to characterize the quality of a fitting through the change of data.</trans> <trans data-src="由上面的表达式可以知道“确定系数”的正常取值范围为[0 1]，越接近1，表明方程的变量对y的解释能力越强，这个模型对数据拟合的也较好">From the above expression, we can know that the normal value range of the "determination coefficient" is [0 1]. The closer to 1, the stronger the explanatory power of the equation variable to y, and the better the model fits the data</trans>

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Fitting toolbox error parameters

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