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谢朝木 · 2021年11月24日

这个题能再把描述结论的形式在说一下吗?

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NO.PZ202106160300004104

问题如下:

Is the relationship between the ratio of cash flow to operations and the ratio of net income to sales significant at the 0.05 level?

选项:

A. No, because the R2 is greater than 0.05

B. No, because the p-values of the intercept and slope are less than 0.05

C. Yes, because the p-values for Fand t for the slope coefficient are less than 0.05

解释:

C is correct. The p-value is the smallest level of significance at which the null hypotheses concerning the slope coefficient can be rejected. In this case, the p-value is less than 0.05, and thus the regression of the ratio of cash flow from operations to sales on the ratio of net income to sales is significant at the 5% level.

这个题我清楚是拒绝B1不等于0的,但题问的是X和Y之间关系在5%下是显著还是不显著,这个问法理解起来就有点绕了。应该是在5%的显著性水平下,B1是显著不等于0的。和答案的如何联系理解?
2 个答案

星星_品职助教 · 2021年11月25日

@ 谢朝木

对的,拒绝原假设=significant(显著),反之同理。

星星_品职助教 · 2021年11月24日

同学你好,

在一元回归方程下,b1是否显著,和Y与X关系是否显著,是同一个意思。

如果b1=0(b1不显著)相当于X无论是多少,都不会对Y产生影响。这也就是Y和X的关系不显著。相反,如果b1≠0(b1显著),那么Y和X之间就有关系。

也可以从C选项中F检验的角度理解,F检验的是方程整体是否显著(即Y和X是否有关系),拒绝F检验的原假设(H0:方程所有系数都同时为0,在一元回归中即b1=0),就相当于方程整体显著,即Y和X之间有关系。


谢朝木 · 2021年11月24日

是否这样理解:如果拒绝原假设,就是显著的。不能拒绝原假设,就是不显著的?

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