线性回归模型的置信区间与预测区间应用分析

Application of Confidence Intervals and Prediction Intervals of Linear Regression

论述线性回归的因变量置信区间和因变量个别值的预测区间原理后,结合实例分析了学生总数与季度营业额2个变量的关系.研究发现,学生总数与季度营业额关系存在很强的正向线性关系(r=0.950 1),可决系数(R2=0.902 7)可以解释总平方和中的90.27%,表明其拟合度很好.之后,给出了因变量平均值的置信区间、因变量个别值的预测区间及图形.

After describing the principle of confidence intervals and prediction intervals, this paper, which applies it to analyze the relationship between such two variables as student size and quarterly turnover, tests regression equation. And the result shows that there exists high degree of fitting between these two variables since there exists a positive linear relationship between the two variables （r=0. 950 1） and about 90.27% of the variation in the quarterly turnover data is explained by student size; The paper of- fers not only confidence intervals for the mean of y and prediction intervals for an individual y by using estimated equation,but some relevant graphs as well.