Estimating the Average Slope
The slope is usually the parameter of primary importance in a simple linear regression. If the straight line model gives a poor fit to the data, one can consider the average slope of the non-linear response. In this paper, we show that if the response is quadratic, then the average slope can be obtained by simply using the slope from a straight line fit. In fact, if the slope of the best fitting line to a smooth non-linear function equals the average slope of the function over an arbitrary interval, then the function must be quadratic. This paper illustrates the case where intentionally fitting a wrong model (in this case, a straight line) gives the correct result (the average slope). The example which motivated this study is used to illustrate the results.
(2003). Estimating the Average Slope. Journal of Applied Statistics, 30 (4), 389-395.