Could you be more specific about what you want? For example, do you want a statistical test with a significance probability or a measure like R^2? Also, are your numbers bounded, e.g., between 0 and 1? What kind of error structure is inherent in the application? Should we think about transforming the response variable or using "glm" or nonlinear regression? If I were concerned about saturation at either end, perhaps the simpliest thing might be to add a cubic to what you considered: x ~ y + I(y^2) + I(y^3) From this we could get significance probabilities for the squared and cubic terms combined. Also, by converting the sum of squares column to percent, we get something like R^2. Hope this helps. Spencer Graves
Paul, David A wrote:
Maybe I'm missing something, but why not use the Pearson Product Moment Correlation Coefficient (r) ? It directly measures the strength of the linear relationship between two variables. A simple approach would be the following: (1) fix a percentage p of the data you are interested in (2) fix one of your two variables (x,y) as a reference - call it x (3) subset your data.frame down to those pairs (x*,y*) corresponding to the middle p percent of x (4) calculate r for the pairs (x*,y*) By doing (1) through (4) many time for increasing values of p I think you'll get what you want. Best, david paul -----Original Message----- From: Luke Whitaker [mailto:luke at inpharmatica.co.uk] Sent: Thursday, April 17, 2003 12:03 PM To: r-help at stat.math.ethz.ch Subject: [R] Measure of linearity between two variables? Hello, I am looking for a measure of linearity in the relationship between two variables. Specifically, I have two variables for which the relationship is reasonably linear over a certain range of values, and then diverges from linearity at either end of the range, as one or other variable "saturates" at a maximum or minimum value. I want to identify the region of linearity, where neither variable has saturated. This is a problem that will be repeated many times so I want a programmatic solution. I am intending to implement some kind of search over the central range of values, expanding out and testing for linearity over each incrementally increased range. However, I need a measure if linearity. So far, I have thought of doing a regression on x ~ y + y^2, and using the absolute value of the ratio of coefficients of the squared and linear terms. Does anyone have any better ideas, either for a linearity measure or a different approach to finding the region of linearity between the two variables ? Thanks, Luke Whitaker
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