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I have a very basic question about interpreting confidence intervals. Say I use R to fit a linear model to the Nile water flow time series (from the datasets package), like this:

# Flow of the Nile river (10^8 cubic metres per year) between 1871-1971
nile.ts <- data.frame(year = do.call(seq, as.list(attributes(Nile)$tsp)),
           flow = as.numeric(Nile))

# Fit linear function 
nile.fit <- gls(flow ~ year, data = nile.ts)

Next, I look at the confidence intervals on the model parameters:

# Look at 95% confidence intervals
intervals(nile.fit)
Approximate 95% confidence intervals

 Coefficients:
                  lower        est.       upper
(Intercept) 4144.217893 6132.173579 8120.129266
year          -3.749313   -2.714305   -1.679298
attr(,"label")
[1] "Coefficients:"

 Residual standard error:
   lower     est.    upper 
132.1041 150.5522 175.0363

Here, the coefficient of year in the model is estimated to be $-2.7$ and has a 95% confidence interval of $[-3.7, -1.7]$. I'd read this as meaning I can be pretty confident that there has been a decline in the flow over time. But what if the confidence interval had been $[-3.7, +1.7]$? Since it straddles zero, does this mean that I can't say anything about the trend? Or, can I state that there is no statistically significant trend?

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1 Answer 1

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Or, can I state that there is no statistically significant trend?

Yes. The coefficient for year would be then not different from 0.

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  • $\begingroup$ @ Lyngbakr, you can use a more formal wording that is based on the p-value in the model output, which is that: the probability that a coefficient estimate will be at least as large as the observed value when the Null hypothesis is true. $\endgroup$ Oct 26, 2017 at 13:51

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