The quadratic regression line
A quadratic regression line can be expressed by the following function:
ŷi = a + b1∙xi + b2∙xi2
Some of you may recognise this as a second degree polynomial function. Note that the independent variable x appears in two different additive terms on the right-hand side of the equals sign, first in its original form xi and then as xi2, which is shorthand for xi∙xi (i.e. xi multiplied by itself).
There are two different b coefficients here, b1 and b2. Both must be computed by the regression analysis program. This is no problem as long as the factors we multiply the coefficients by (here xi, and xi2) are not too strongly correlated with each other. Unfortunately, the original year of birth variable and that variable’s squared version are too strongly correlated, but this problem can be reduced if we deduct 1900 from the variable values of every person in the dataset, thus making birth year a two-digit variable with values starting at 5 instead of 1905. This has already been done for you in the specially prepared ESS EduNet regression module data set. You must do it yourself if you analyse other ESS data sets.