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WYP · 2021年02月01日

为什么p-value能反映两个变量的relationship?

NO.PZ2015120204000006

问题如下:

The independent variable is the ratio of net income to sales for restaurants with a market cap of more than $100 million and the dependent variable is the ratio of cash flow from operations to sales for those restaurants.

Is the relationship between the ratio of cash flow to operations and the ratio of net income to sales significant at the 5 percent level?

选项:

A.

No, because the R-squared 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 F and t for the slope coefficient are less than 0.05.

解释:

C is correct.

The p-value reflects the strength of the relationship between the two variables. In this case the p-value is less than 0.05, and thus the regression of the ratio of cash flow fromoperations to sales on the ratio of net income to sales is significant at the 5 percent level.

The p-value reflects the strength of the relationship between the two variables. 这句话不理解。针对题目最后的问题,为什么是看p来判断呢

1 个答案

星星_品职助教 · 2021年02月02日

同学你好,

“The p-value reflects the strength of the relationship between the two variables.”这句话实际上想说的就是可以根据p-value去判断是否要拒绝原假设。如果拒绝了原假设,说明两个变量之间是有关系的(显著不为0/significant);如果不能拒绝原假设,则两个变量之间是没关系的(not significant)。

根据p-value去判断是否要拒绝原假设的方法是“p越小越拒绝”,即p-value<α时,直接拒绝原假设。

本题α=5%,无论是F还是t的p-value=0,所以拒绝原假设。说明 ratio of cash flow to operations(dependent variable )和the ratio of net income to sales(independent variable )这两个变量之间是有关系的

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NO.PZ2015120204000006 No, because the p-values of the intercept anslope are less th0.05. Yes, because the p-values for F ant for the slope coefficient are less th0.05. C is correct. The p-value reflects the strength of the relationship between the two variables. In this case the p-value is less th0.05, anthus the regression of the ratio of cash flow fromoperations to sales on the ratio of net income to sales is significant the 5 percent level. 解析只说了p小于0.05

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