Polynomial regression is the answer for these data and for most curvilinear data that either show a maximum or a minimum in the curve, or that could show a max or min if you extrapolated the curve beyond your data. Often the different points come from the same subjects, especially when time is the independent variable. You can still fit polynomials to such data, but you have to use repeated-measures models . I deal with repeated-measures polynomials later, but the interpretation of the numbers describing the shape of the curve is the same, and I deal with that here. 2 N otice the subtle difference from the model for multiple linear regression on the previous page .
Polynomials are a special case of the more general non-linear models .
If the curve is trends up again at one end, you'll need a cubic model. Curves with multiple kinks need even higher-order terms. It's rare to go past a quadratic, though. For the data in the figure, b would represent the change in attitude per year of experience. Remember that you can derive these coefficients or parameters as raw values, as percents, and as normalized regression coefficients, just like the slope in a simple linear regression .