# Chapter 3: Non-linear associations

In the previous chapter, we assumed that associations between variables could be described by a straight line (or a linear function). The assumption was not unwarranted. The Norwegian mean education length seemed to have been rising at a relatively constant long-term rate. Thus, it made sense to represent it as a linear function of peoples’ birth year.

The Swedish sample, however, does not fit quite so well with the linear model. As shown in Figure 8, the line that indicates the cohorts’ mean education lengths tends to be above the linear regression line for those born between 1940 and 1960, and below the line for the rest. Thus, the growth of the mean education length seems to have decreased over time. The fit of the regression line is better than in the Norwegian case (R^{2} is 0.2), but in the Swedish case the fit can be made even better by adapting a curved regression line instead of a linear one. Some types of curved lines can be fitted with the OLS method. These regression lines are called curvilinear, and one such type, the quadratic regression line, is particularly popular because of its relative flexibility. It accommodates a wide range of different curve shapes.

Figure 8. Scatterplot with linear regression line. Swedish ESS data