问题如下:
After doing the regression analysis, Jacky finds that there exist some observations which have big residual values that influence the regression results. Then he takes them away from the total sample and does the regression analysis again. What do Coefficient Determination and Standard error of estimate change?
选项:
A. Coefficient Determination will increase, Standard error of estimate will increase.
B. Coefficient Determination will decrease, Standard error of estimate will increase.
C. Coefficient Determination will increase, Standard error of estimate will decrease.
解释:
C is correct.
考点: Coefficient of Determination & Standard Error of Estimate.
解析: 当Jacky删除了那些残差比较大的样本后,模型的误差就变小了,说明模型更加精确了。所以这个模型的标准误(Standard error of estimate)就会变小。模型的误差变小同时也意味着模型的拟合优度变优了,也就是说模型的解释力度变大了,所以Coefficient Determination 也就是变大了。所以选择C选项。
老师,我可以理解成去除有影响的项,sample变小,sse变小,根据r方公式=1-sse/sst得出变大,这样理解对吗?