简单回归分析_simple linear regression.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,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,线反映,x,与,y,的线性依,存规律。,y ,x,Simple linear regression,Scatter plot,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、,Basis theory,1.data format,i x y,1 x,1,y,1,2 x,2,y,2,.,n,x,n,y,n,Simple linear regression,2.,error,question,第,i,个个体的误差为,：,i,=(a+,b,x,i,)-,y,i,所有,n,个个体的误差为,：,|,i,|,i,2,=,I,从而，所求直线,即使得,I,为最小,b=,L,xy,/,L,xx,a=y-,bx,求最小值点,Simple linear regression,L,xx,-,Recall,the sum of squares of deviations,from the mean,L,xy,-,Recall,the sum of the cross products,of deviations 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,：,t,b,=(,b,-0)/,s,b,其中，,s,b,2,=,ss,剩,/(（,n-2）,L,xx,)，v=,n,-2,residual,ss,剩,=,L,yy,-,b,L,xy,2.,coefficient of determination,R,2,=,regression,ss,回,/,t,otal,ss,总,=,b,L,xy,/,L,yy,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,