How to determine whether a data set is continuously growing? I sampled some data at certain sampling rate (e.g., 1 sample per minute). I want to know whether the values in this data set are continuously growing or they are just fluctuating around certain value. How can I do that?
In addition, I would like to predict the future values to be sampled. Based on the prediction (whether it will grow along with certain confidence level), I can decide whether to continue the experiment to sample more data or simply stop the experiment.
Update: I think this is exactly what I need: Trend Esitmation
Note: I know very little (if not nothing) about statistics, so bear with me and do correct me if you find me using wrong terminology.
 A: One way to do this would be to regress on time. What software are you using?
This is a very simple approach that doesn't allow for effects other than a continuous effect of time. In R you could do something like this.
time <- 1:10
values <- c(2,4,5,7,5,6,8,10,11,10)
m1 <- lm(values~time)
summary(m1)

but you will probably have more values (and times) and you may be reading from some other file, which would change things. 
summary(m1) yields

Call: lm(formula = values ~ time)

This just says what m1 is.

Residuals:
      Min      1Q  Median      3Q     Max 
  -1.3455 -0.8455  0.1091  0.8136  1.5636 

This gives some info about the residuals. You can get more with plot(m1). Ordinary least square regression assumes some things, including that the residuals are normally distributed with constant variance.

Coefficients:
Estimate Std. Error t value Pr(>|t|) 
(Intercept)   1.8000     0.7412   2.428   0.0413 *  
time          0.9091     0.1195   7.610 6.25e-05 *

this tells you the model that is estimated by m1: value = 1.8 + .91*time. It also give the standard errors of the coefficients (0.74 and 0.12), their t-values and their statistical significance. 

Residual standard error: 1.085 on 8 degrees of freedom Multiple
  R-squared: 0.8786,     Adjusted R-squared: 0.8635  F-statistic: 57.92
  on 1 and 8 DF,  p-value: 6.245e-05

If you want to do more complex things, let us know more about your problem.
A: The idea that Trend Estimation might be appropriate is in the right direction but very very far from the answer. In practice one doesn't know how many trends there or the length of the (each) trend , in fact one wants to discover them. One doesn't know if there are level/step shifts and how many and the length of each step. Step shifts are intercept changes which can confuse trend detection schemes which is why you need to find procedures which suggest both kinds. Distinguishing between Outliers and Inliers is an important consideration in trend/level detection. If the observed series is auto-correlated then this often masks or falsely suggests trend/level structure. One has to integrate ARIMA memory and Intervention Detection procedures to answer the question about trends and steps. Fitting splines is rather useless as one doesn't know how many local splines there are and the length of the spline . Now not to further complicate this already complicated answer error variance change or ARIMA model parameters may change over time causing both false negatives and false positives with respect to trend/steps. The solution is to implement software that deals with all of these possible states of nature and parsimoniously delivers a uselful model with useful conclusions regarding trends/steps.pulses and seasonal pulses. See http://www.unc.edu/~jbhill/tsay.pdf for a discussion. 
