It's not the inherent quality of the data. Whether you want to treat the variables equally or not depends on the objective. Here you're minimizing a vertical distance from $y_i$ to $y(x_i)$, where y-axis is latitude and x-axis is a longitude. The trend line that you got from Excel is as a common sense as the eigen vector from PCA when you understand that in the Excel regression the variables are not equal. Here's how you could do it in R: > para plot(para) you draw a perpendicular to a line, and minimize the sum of those for each observation. You can think of it as a line minimizing the shortest distance from any given $(x_i,y_i)$ point to a line itself, i.e. In particular, it's one of the eigen vectors of the covariance matrix of these variables. The latter can be obtained by applying PCA. The trend line in Excel is from the regression of the dependent variable "lat" on independent variable "lon." What you call a "common sense line" can be obtained when you don't designate dependent variable, and treat both the latitude and longitude equally. This is an interesting thread and It would be a shame for the data to be lost and someone in future unable to reproduce the examples, so I'm adding it as a comment here (which is the data from the following link). I'm an engineer, NOT a mathematician or statistician, so the information in these responses has given me a lot more areas for research. The final objective is to investigate how wind strength and direction varies with height. The data represent a paraglider climbing in a thermal whilst drifting with the wind.
Are the type1 and type2 regression techniques available as excel functions?
An Excel spreadsheet with data and graph is available here:Įxample data, CSV in Pastebin.
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