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?