Re: TDist Formula and Explanation

Thanks for the post. It will certaintly serve as a
good source for
reference. However, I'm still struggling with
implementing the nuts
and bolts of the formula to come up with a valid
result. I've tried
to use the incomplete beta function to calculate the
p-value, but I'm
still getting skewed results. Using the results
listed below I find
that a = 0.5, b=9, x'=.894102 (using the formula:
(df_Regression * F
Statistic)/(df_Regression * F Statistic +
df_Residual). These values
should (I think) be my input to the incomplete beta
function.
However, when I put these inputs into the formula I
get results that
are consistently high. Is there something that you
see that I'm doing
incorrectly? If not, is there some guidance you
could provide on how
to use the formula?

X Y
28 5.2
26 5.1
32 5.6
24 4.6
54 11.3
59 8.1
44 7.8
30 5.8
40 5.1
82 18
42 4.9
58 11.8
28 5.2
20 4.8
42 7.9
47 6.4
112 20
85 13.7
31 5.1
26 2.9



I put your data into Minitab. I get y = -0.412 + 0.184*x as the fitted regression.

The standard error of beta is 0.1493 and t = 0.184/0.1493 = 12.3

With 18 degrees of freedom, Excel calculates the right tail probability as 1.64E-10 if it's a one-sided test and 3.28E-10 if it's a two-sided test.

If your problem is to calculate small tails (i.e., large t), those expansions in A&S might turn out to be pretty accurate.

BTW, I had a problem downloading A&S online, but I still have the hard copy.

Jack
.

Relevant Pages

  • Re: TDist Formula and Explanation
    ... and bolts of the formula to come up with a valid ... to use the incomplete beta function to calculate the ... BTW, I had a problem downloading A&S online, but I still have the hard copy. ...
    (sci.stat.math)
  • Re: TDist Formula and Explanation
    ... and bolts of the formula to come up with a valid ... to use the incomplete beta function to calculate the ... Re the OP's question about how to compute the p-value in Excel: ...
    (sci.stat.math)
  • Re: How to integrate a function from -inf to a ?
    ... (Just bitching.) ... the incomplete beta function. ... Since matlab supplies the incomplete beta ... preferably the same, cat. ...
    (comp.soft-sys.matlab)