组间平方和 (SSR:Sum of squares of the regression):预测数据与标签均值之间差值的平方和。 公式:SSR = \Sigma (\bar{y_{i}}-\hat{y_{i}})^{2} 离差平方和(SST:Total sum of squares):实际值和均值之间的差值的平方和。 公式:SSR = \Sigma (\bar{y_{i}}-y_{i})^{2} 得到,R^{2}=\f...
回归平方和(SSR,Sum of Squares forRegression):因变量的回归值(直线上的Y值)与其均值(给定点的Y值平均)的差的平方和,即,它是由于自变量x的变化引起的y的变化,反映了y的总偏差中由于x与y之间的线性关系引起的y的变化部分,是可以由回归直线来解释的 残差平方和(又称误差平方和,SSE,Sum of Squaresfor Error)...
1·SST(Sum of Square Total):(Yi为实际值,Ybar为均值) 2·SSR(Sum of Square Regression):(Yhat为预测值) 3·SSE(Sum of Square Error):(下图也表示了这三者之间的关系) 计算出上述值之后,我们在实际中常用RMSE去评价(越接近于1越好): Ps:当然还有MAE、MSE、(R‘)^2等可以很好的评价这个模型的好坏。
vpa(cov_alpha_beta,6) %%SST,SSE和SSR disp('SST:'); SST = YY_s_m Y_OLS = reshape(alpha+beta*X',1,n); disp('SSR:'); SSR = (Y_OLS-Expection(Y,1))*(Y_OLS-Expection(Y,1))' disp('SSE:'); SSE = (Y-Y_OLS)*(Y-Y_OLS)' function En = Expection(M,n) %%n阶原点矩%...
SSE—Sum of squared errors numeric value SSR—Regression sum of squares numeric value SST—Total sum of squares numeric value Fitting Method Robust—Robust fit information structure Steps—Stepwise fitting information structure Input Data Formula—Model information ...
Since Y and e are independent (i.e. cov(Y,e) = 0), var(Y ) = var(Y + e) = var(Y) + var(e) This leads ton∑i=1(Yi Y)2 =n∑i=1(Yi Y)2 +n∑i=1e2i 18Decomposing the Variance – ANOVA TablesSSR: Variation in Y explained by the regression line. SSE: Variation in...
Chi-square distribution可以说是linear regression中最重要的工具,它是用来构建各种检验的一个重要量。我们知道SST = SSR + SSE, 这三个都是Chi-square distribution,那么他们的自由度有代表了什么呢?SST= sum(y-ybar)^2,它的自由度是n-1,因为它本来可以有n个,但y-bar的出现,对它多了一层限制。SSE的自由...
十一章简单线性回归SimpleLinearRegression
Steps: run two regression for each hypothesis, one for the restricted model and one for the unrestricted model. The SST should be the same across the two models. What is different is SSE and SSR. That is, what is different is R2. Let ; Use the following formulas: or (proof: use ...
1、学习-好资料Class4:Inferenceinmultipleregression.I.TheLogicofStatisticalInferenceThelogicofstatisticalinferenceissimple:wewouldliketomakeinferencesaboutapopulationfromwhatweobservefromthesamplethathasbeendrawnrandomlyfromthepopulation.Thesamples'characteristicsarecalled"pointestimates."Itisa 2、lmostcertainthatthe...