# What type of non-linear regression would you use on this data

I am trying to model a wind turbine power curve, or in other words, given the windspeed (X), I would like predict the produced power (Y). I want to use historical data to estimate this model. You can read more about the power curve here: http://www.windpowerwiki.dk/index.php?title=Power_curves. On the given rescaled power curve below, the power can never go below 0 and never above 4, and the windspeed can never go below 0.

Question 1: What type of model would you use to predict Y with X (the red line on the plot is a LOESS fit)?

Question 2: Is it possible, in your suggested model, to use lagged variables of Y? The dots on the graph are measurements over time, so if one point is above the red line, it is very likely that the next measurement in time is also above the red line (this is because another important predictor, air pressure, is not included in the model, so I assume there is important autocorrelation). How can I take this into account?

Thank you!

• (1) "Lagged" in what sense? This does not appear to be any definite series of data. (2) A good choice of model depends on the nature of the data: one would use two quite different models depending on whether $X$ were considered to be measured with substantial error or not, for instance. As another example, one would also choose different models depending on how the truncation of $Y$ at $0$ and $4$ occurs: are these natural limits or artificial cutoffs? Please edit your question to provide more information about the data so that it can be answered appropriately. – whuber Feb 20 '14 at 17:30
• (1) what have you thought of? and why don't you like those approaches (2) lagged y? is this a time series? (3) the issue - to me - seems not to be the prediction, the giving honest estimates of variance around mean. – charles Feb 20 '14 at 17:35
• Y appears to be bounded above and below. What is Y? – Glen_b Feb 20 '14 at 22:40
• @whuber I hope my edit contains the extra information you requested? Would you like to give my question a second thought? Thanks a lot. – Kasper Feb 21 '14 at 13:12