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See the images below….anyone please explain to me why the DF test is rejected for ‘outline air temperate and ‘assembly line speed’… when test statistic values are NOT < t critical? am i reading it wrong? DF test fails to reject 'defective assembly per hour', i could understand that because test statistics > tcritical.

hmmmm I am not 100% confident in this answer but the DF test is to test for a unit root and that the slope coefficient is equal to 1. Clearly outline air temp and assembly line speed can be rejected if they are approximately 5 and 13 standard deviations away from 1. Defects, however, we cannot say that they are statistically different from one.

I am not entirely following.. 🙁 the rule is reject null when t > + t critical, or t <  t critical. (see the 2nd image) for example on air temp, tcritical is 5.8, and test stat is 0.4, it doesnt satisfy this reject if 't <  t critical'.... i dont understand why it rejected. pls pls help!!!

i understand this ‘if the absolute Tvalue is bigger than the critical Tvalue of reference, one must reject the null hypothesis.’
so taking the air temp example, 0.4 is not greater than 5.8… how come the answer is reject the null??? i am so confused!! please help me understand this!! thank you!!

I think your not understanding the table. The first column is the absolute distance each coefficient/beta is from 1 in the regession. Dickey Fuller test is b11=0 and we want to reject the null being =0 becaue if b1 (slope/beta) is 1 then 11 is 0 and we will have a unit root bease the null bring 0 is how dicky fuller defines it for this test. To clarify look at outside air temp with a test statistic of .423. That is how far b1 is from 1 or b11= .423. So the slope coefficient must be .577…. to check my work( .5771=.423). Second column has the standard errors. So dividing column 1 by column 2 gives us the tstat, or the number of deviations we are from zero, which is column 3. If this number is more than our critical t stat, that we need to look up on a t table but is close to 1.96 @ a 5% significance, then we can say it’s not equal to 0 or that b1 does not = 1 which is the definition of a unit root. When you say outside air temp .4 is less than 5.8 your using wrong numbers. 5.8 is the t stat, numbers deviations from 0, and u need to compare that to the critical t stat that is about 1.96 that you need to look up.




I actually like how that table is presented. Something you’d CFAI do on the real exam. Everyone is SO accustomed to seeing the table the same way. Coefficient first, then standard error then t stat. They just changed one column and used different terminology to show you understand the concepts and didn’t just memorize tables.


Just to make sure we are on the same page, that image is not a dickey fuller test. That’s just a general ttest for a slope coefficient from the regression. To run the DF test on that slope coefficient you would take .641= .36. Then .36/.26= 1.385 is your tstat which is not significant so you could say it has a unit root. This is if the regression is an AR model of course.




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