简单回归分析-simplelinearreg.ppt

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1、Simple linear regression一、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+bxindependent variabledependent variablexyregression coefficientor slopebintercepta二、二、Basis thought 寻找一条最佳直线反映x与y的线性依

2、存规律。y xSimple linear regressionScatter plotz 所求直线使得理论值与实际观察值最接近 用直线去描述这些观察点时，使得error Least!三、三、Basis theory1.data format i x y 1 x1 y1 2 x2 y2 .n xn ynSimple linear regressionz2.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，所求直线从而，所求直线即使得即使得I 为最小为最小zb=Lxy/Lxxza=y-bx 求最小值点Simple linear

3、regressionzLxx-Recall the sum of squares of deviations from the meanzLxy-Recall the sum of the cross products of deviations from the mean Simple linear regressionz三、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、四、Testing th

4、e Significance of a regression1.t-Testing：tb=(b-0)/sb 其中，sb2=ss剩/(（n-2）Lxx)，v=n-2 residual ss剩=Lyy-b Lxy2.coefficient of determination R2=regression ss回/total ss总 =b Lxy/Lyy3.F-Testing：F=MS回/MS剩五、五、Confidence intervals in regression1.1.Confidence intervals for an Estimated y(预测)：2.已知自变量x去估计反应变量y。3.(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 regression2.prediction interval(预报)：已知反应变量y去估计自变量x。Simple linear regressionSimple Linear Correlation一、The correlation coefficient:Simple linear Correlation二、t-Testing:Simple linear Correlation