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数理统计上机 报 告上机实验题目:用R软件进行一元线性回归上机实验目的:1、 进一步理解假设实验的基本思想,学会使用实验检验和进行统计推断。2、 学会利用R软件进行假设实验的方法。一元线性回归基本理论、方法:基本理论:假设预测目标因变量为Y,影响它变化的一个自变量为X,因变量随自变量的增(减)方向的变化。一元线性回归分析就是要依据一定数量的观察样本(Xi, Yi),i=1,2,n,找出回归直线方程Y=a+b*X方法:对应于每一个Xi,根据回归直线方程可以计算出一个因变量估计值Yi。回归方程估计值Yi 与实际观察值Yj之间的误差记作e-i=Yi-Yi。显然,n个误差的总和越小,说明回归拟合的直线越能反映两变量间的平均变化线性关系。据此,回归分析要使拟合所得直线的平均平方离差达到最小,据此,回归分析要使拟合所得直线的平均平方离差达到最小,简称最小二乘法将求出的a和b代入式(1)就得到回归直线Yi=a+bXi 。那么,只要给定Xi值,就可以用作因变量Yi的预测值。(一)实验实例和数据资料:有甲、乙两个实验员,对同一实验的同一指标进行测定,两人测定的结果如下:实验号12345678甲4.33.23.83.53.54.83.33.9乙3.74.13.83.84.63.92.84.4试问:甲、乙两人的测定有无显著差异?取显著水平=0.05.上机实验步骤:(1) 设置假设:H0:u1-u-2=0:H1:u1-u-20(2) 确定自由度为n1+n2-2=14;显著性水平a=0.05(3) 计算样本均值样本标准差和合并方差统计量的观测值alpha-0.05;n1-8;n2-8;x-c(4.3,3.2,3.8,3.5,3.5,4.8,3.3,3.9);y-c(3.7,4.1,3.8,3.8,4.6,3.9,2.8,4.4);var1-var(x); xbar-mean(x); var2-var(y); ybar-mean(y); Sw2-(n1-1)*var1+(n2-1)*var2)/(n1+n2-2) t-(xbar-ybar)/(sqrt(Sw2)*sqrt(1/n1+1/n2);tvalue-qt(alpha,n1+n2-2);(4) 计算临界值:tvalue-qt(alpha,n1+n2-2)(5) 比较临界值和统计量的观测值,并作出统计推断实例计算结果及分析:alpha n1 n2 x y var1 xbar var2 ybar Sw2 t var11 0.2926786 xbar1 3.7875 var21 0.2926786 ybar1 3.8875Sw21 0.2926786 t1 -0.3696873 tvalue1 -1.76131分析:t=-0.3696873tvalue=-1.76131,所以接受假设H1即甲乙两人的测定无显著性差异。(二)实验实例和数据资料:2.某型号玻璃纸的横向延伸率要求不低于65%,且其服从正态分布,现对一批该批号的玻璃纸测得100个数据如下: (x%横向延伸率)35.537.539.541.543.545.547.549.551.553.555.557.559.561.563.5频数7811991217145320201上机实验步骤:(1)设置假设:H0:u=65, H1:u65.(2)确定自由度为n=100-1=99;显著性水平a=0.05(3) 输入数据x-c(35.5,35.5,35.5,35.5,35.5,35.5,35.5,37.5,37.5,37.5,37.5,37.5,37.5,37.5,37.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,41.5,41.5,41.5,41.5,41.5,41.5,41.5,41.5,41.5,43.5,43.5,43.5,43.5,43.5,43.5,43.5,43.5,43.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,51.5,51.5,51.5,51.5,51.5,53.5,53.5,53.5,55.5,55.5,59.5,59.5,63.5)(4)用R软件计算临界值(5)比较临界值和统计量的观测值,并作出推断实例计算结果及分析:计算过程如下:alpha-0.05;n-100; x-c(35.5,35.5,35.5,35.5,35.5,35.5,35.5,37.5,37.5,37.5,37.5,37.5,37.5,37.5,37.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,39.5,41.5,41.5,41.5,41.5,41.5,41.5,41.5,41.5,41.5,43.5,43.5,43.5,43.5,43.5,43.5,43.5,43.5,43.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,45.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,47.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,49.5,51.5,51.5,51.5,51.5,51.5,53.5,53.5,53.5,55.5,55.5,59.5,59.5,63.5)sd1-sd(x); xbar-mean(x);t-(xbar-65.0)/(sd1/sqrt(n); tvalue-qt(alpha,n-1); sd11 5.815896xbar1 45.06 t1 -34.28534tvalue1 -1.660391分析推断:因为t=-3
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