《简单回归分析simple linear regression演示教学》由会员分享，可在线阅读，更多相关《简单回归分析simple linear regression演示教学（14页珍藏版）》请在金锄头文库上搜索。
1、Simple linear regression,一、Concept and maths model： The simplest functional relationship of one variable to another in a population is the simple linear regression. X and Y model y=a+bx,independent variable,dependent variable,x,y,regression coefficient or slope,b,intercept,a,二、Basis thought 寻找一条最佳直
2、线反映x与y的线性依 存规律。,y x,Simple linear regression,Scatter plot,2.error question 第i个个体的误差为： i =(a+bx i )-yi 所有n 个个体的误差为： |i | i2=I 从而，所求直线 即使得I 为最小,b=Lxy /Lxx a=y-bx 求最小值点,Simple linear regression,Lxx -Recall the sum of squares of deviations from the mean,Lxy -Recall the sum of the cross products of devia
3、tions from the mean,Simple linear regression,三、 Basis method： method of least squares(最小二乘法)，即 在线性回归分析中，估计模型的参数时，保证 the error sum of squares最小的原则。,Simple linear regression,四、Testing the Significance of a regression,1. t-Testing ： tb=(b-0)/sb 其中，sb2=ss剩/(（n-2）Lxx)，v=n-2 residual ss剩= Lyy- b Lxy 2.coe
4、fficient of determination R2= regression ss回/total ss总 =b Lxy/Lyy 3. F-Testing ： F= MS回/MS剩,五、Confidence intervals in regression 1. Confidence intervals for an Estimated y(预测)： 已知自变量x去估计反应变量y。 (1) 的估计(条件平均值的100(1)%可信区 间 ):,Simple linear regression,(2)个体Y值的100(1)%容许区间:,Simple linear regression,2. prediction interval(预报)： 已知反应变量y去估计自变量x。,Simple linear regression,Simple Linear Correlation,一、The correlation coefficient:,Simple linear Correlation,二、t-Testing:,Simple linear Correlation,
