Hello,
Here is a question where I dont not understand the table entierly. Why do they need to show a column with significiqnce of T and F? What does that mean please?
http://tinypic.com/view.php?pic=14e6tdu&s=8#.U2z_9_mSyK8 Thx a lot
“significance of T” and “significance of F” in this case appear to be the same thing as “p value of t” and “p value of F” as they appear in the CFAI books … which signifies the lowest level of significance for the t and F values at which the null hypotheses can be rejected.
As Swat stated, these significance values are often called observed significance levels or p-values. Additionally, a p-value is the probability of seeing results MORE contradictory to the null hypothesis than the results at hand (assuming a true null). Those are p-values. The p-values for the t-tests allow you to test an individual term in the regression (for example LagI) to determine the statistical significance of the variable. The p-value for the F-statistic is used when testing the entire model (statistical) utility.
The null hypothesis for this test is that none of the terms (exclude the intercept from this) are statistically different from zero.
The alternative hypothesis is that at least ONE of the terms is statistically different from zero, implying that the model is statistically useful.
Take note that in simple linear regression (SLR) you only have one independent variable. The t-statistic, in this case, is actually the square root of the F-statistic-- ONLY in simple linear regression. So, the same information can be taken from these test statistics in terms of the overall model utility. When you enter multiple regression this is not the case. Keep in mind, though, that the t-test allows us to perform a one-tailed test and the F-test does not.
Hi Swat and Ticker, Thx for your answer. Very nice. So how do you interpret p=0? I believe the small the more sure we can reject the Null hypothesis right? Thx
Yes. If you recall rejection regions: any test statistic that is beyond the boundaries of a rejection region, outside of (-1.96,+1.96) for example (alpha= 0.05), indicates statistically significant results (reject the null hypothesis). This is cumbersome to use tables or memorize critical values, so software packages will report the p-value associated with the calculated test statistic. If you select an alpha of 0.05 and the p-value is less than this, you can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.
Again, if you recall, alpha is a threshold that you select. This is the maximum probability of a Type I error that you are comfortable with for the test (0.05 is 5%). So a p-value of .03 means I COULD pick an alpha of 0.03 and still reject the null hypothesis, but this is a bad practice. In short, pick an alpha value prior to seeing results (standard convention dictates no more than 0.10 or 10%) or use the alpha level the question says you should use. If the p-value is less than this alpha level, reject the null hypothesis. If the p-value is greater than the selected alpha, you have insufficient evidence to reject-- therefore, you fail to reject the null.
Lastly, be careful rounding p-values, i.e., don’t do it. Here, it is of no consequence, but other times it might be. I have seen many people round a p-value of 0.0503 to 0.05 (for example), but this is wrong. They should fail to reject the null at an alpha of 0.05 (since p-value exceeds alpha), but they instead round the p-value and reject the null— wrong approach.
Hope this helps!
Wow great answer. Thx a lot. I needed the review =) You mqde things much clearer.
No problem, glad it helped!
This statement is incorrect no? An F-stat is always a one-tailed test.
No, but I wasn’t very clear. The meaning of my statement was that a t-test will allow for a one-tailed (uni-directional) test (i.e. an alternative hypothesis of b1<0) where the F-test in this setting will not allow for such a test (it is testing the hypothesis that b1=b2=…=bi=0 with the alternative being that at least 1 coefficient is different from zero).
I hope this is clear now.
Edited for clarity