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# P1.T2., Stock & Watson Single Regression: Hypothesis Tests and Confidence Intervals

#### elena77

##### New Member
Subscriber
Hi David,

I need to understand how p-value is derived.
On your study note for tutorial video for the captioned p.12, please explain how we get CDF of 0.9878 for p-value calculation. Similarly, please show calculation for 2-sided p-value in following two slides p.13 (1.34%) and p.14 (4.10%). Thank you.

Best regards,
Kaori

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Kaori Ide FYI, I'll be focused on updating content (extremely time consuming) thru end of year so won't be very active in forum support until after the New Year, especially if the topic is repetitive. We already have a lot of discussion on p values (search "p-value") and please do take a look at my video "The p value is the exact significance value" https://www.bionicturtle.com/forum/threads/t2-12-the-p-value-is-the-exact-significance-level.21998/

In regard to this example, the p-values are given in Excel by
• T.DIST.2T(2.646, 27) = 1.34% where 2.646 = (23.25 - 18.5)/[9.5/sqrt(28)]; i.e., t = (X - µ)/SE where the standard error (SE) = 9.5/sqrt(28)
• T.DIST.2T(2.100, 49) where 2.100 = (23.25 - 18.5)/[16/sqrt(50)] where SE = 16/sqrt(50)
The p-value returns to area in the tail(s) given a quantile; i.e., only 1.34% of the area is in the tails to the left/right of +/- 2.646, so you can use the lookup table to similarly approximate. Thanks,