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Science Forum Index » Statistics - Math Forum » linear fit, is my slope significant at 95% level?
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| Charlie |
 Posted: Sat Mar 17, 2007 2:21 pm |
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Guest
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Hello all, I'm working with some temperature data, which I've done a
linear fit to, and ploted 95% confidence intervals using +/- 2
standard deviations.
I am trying to determine if the slope of my linear fit is significant
at the 95% level. I believe this means my null hypothesis would be
'slope not equal to zero' and my alternative would be 'slope equal to
0'
Its been many many years since I've done statistics... if someone out
there could explain to me a procedure for going about this, it would
be great.. or if you could point me towards some good online notes it
would also be good.
cheers,
- Charlie |
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| Jack Tomsky |
| Posted: Sat Mar 17, 2007 2:42 pm |
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Quote: Hello all, I'm working with some temperature data,
which I've done a
linear fit to, and ploted 95% confidence intervals
using +/- 2
standard deviations.
I am trying to determine if the slope of my linear
fit is significant
at the 95% level. I believe this means my null
hypothesis would be
'slope not equal to zero' and my alternative would be
'slope equal to
0'
Its been many many years since I've done
statistics... if someone out
there could explain to me a procedure for going about
this, it would
be great.. or if you could point me towards some good
online notes it
would also be good.
cheers,
- Charlie
The null hypothesis is that the population slope is zero and the alternative hypothesis is that the population slope is not zero. The test is a t test, in which the test statistic is the estimated slope divided by its estimated standard error. Incidentally, the conventional significance level is 5%.
Jack |
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| David Winsemius |
| Posted: Sat Mar 17, 2007 5:48 pm |
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"Charlie" <charliebishop@gmail.com> wrote in news:1174159285.137135.309900
@l77g2000hsb.googlegroups.com:
Quote: Hello all, I'm working with some temperature data, which I've done a
linear fit to, and ploted 95% confidence intervals using +/- 2
standard deviations.
What method did you use to make your fit?
Quote:
I am trying to determine if the slope of my linear fit is significant
at the 95% level. I believe this means my null hypothesis would be
'slope not equal to zero' and my alternative would be 'slope equal to
0'
The usual method is to make H0: slope = 0 and HA: slope <> 0.
That is because the test statistic is typically designed so that it will be
minimized when the null is true.
Quote: Its been many many years since I've done statistics... if someone out
there could explain to me a procedure for going about this, it would
be great.. or if you could point me towards some good online notes it
would also be good.
The usual approach would be to use a stat package to calculate a regression
line. The default output will usually have a coefficient which would be the
slope and a standard error of the estimate. You would see whether the CI
formed by coeff +/- 1.96 SE(coeff) included zero or not. If it does not
include zero then you can say that H0 is rejected at a significance level
of 0.05 using a two-sided test.
Lately Wikipedia seems to have reasonably useful stats pages. I am not
exactly sure what you mean by "explain to me a procedure". Do you want a
worked example. If so, then limit your searches to domains with .edu at the
end and search on "hypothesis tests" and "simple linear regression".
--
David Winsemius |
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