# Confidence intervals on model parameters

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?

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