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I'm new to statistics, so I'm having some trouble interpreting some results.

Let's say I was interested in creating a daily wind speed profile for the arctic during a 30 day period. I have 5 different weather stations setup to measure x and y wind speed. The x and y wind speeds are independent, and both are normally distributed with a 0 mean and equal variance. This produces a Rayleigh distribution for the magnitude of the overall wind vector.

If I collected 4 data points per minute, over 30 days, from minute 0 to 1 I would have 120 data points for one station. If I were to average all of these together, I would get one data point for each station with some variance at every minute. So from minute 0 to 1 I now have 5 data point, which are each the mean of 120 data points. Now I perform regression analysis on the 5 sets of curves I've created from the averaging, since I expect each wind profile to be similar. How do I incorporate the variance in each average data point? Does the fact that the points come from a Rayleigh distribution, rather than a normal distribution, have any effect on the regression analysis? My understanding is that as long as the residuals are normally distributed, all confidence interval measures are valid. This will be a nonlinear regression model, is the Durbin-Watson statistic still valid? I also see things like F tests and T tests applied to linear regression, can the apply to nonlinear regression?

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  • $\begingroup$ What are "x and y wind speeds"? How can wind speed be normally distributed at all, much less with a mea of 0? Why would you average some of these wind speeds? What is the regression you want to perform? You should consider not averaging the data but using either multi=level models or time series analysis. $\endgroup$ – Peter Flom Jul 5 '13 at 21:55
  • $\begingroup$ x and y wind speeds would be the vector components defined by some coordinate system. The wind speed cannot be normally distributed but the vectors can, sometimes the wind blows left and sometimes it blows right. I am averaging the data points just to reduce the size of the data. In reality, I have millions of data points over a one minute time span. I'm not experienced in data analysis so this might be an amateur attempt to simplify the data. The regression I want to perform should tell me wind speed as a function of time. $\endgroup$ – user27606 Jul 8 '13 at 15:52
  • $\begingroup$ Well, not to be snide, but I think maybe you need to consider hiring an expert. You have a combination of spatial data and longitudinal data - each area is complex. The intersection is more complex. $\endgroup$ – Peter Flom Jul 8 '13 at 16:32
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I would agree that if the residuals are normally distributed everything is ok But are your residuals normally distributed? I would have thought the floor at zero (ie magnitudes nonnegative) would stop residuals being normal ( unless its always windy...)

its perhaps useful for you to learn how to bootstrap/run monte carlo to check all these things

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