Appendix

Quadratic functions (second degree polynomials), see chapter 3

Here are some examples that demonstrate the curve shapes that can be created by means of quadratic functions. For instance, Figure A2 presents the curve that corresponds to the function y = 6 - 2∙x + 0.5∙x2. It descends towards the right for low values of x. The reason is that, for these values, the negative term - 2∙x dominates over the positive term + 0.5∙x2. But for higher values of x, the positive term dominates over the negative one, because the value of the squared x becomes much higher than the value of x and, consequently, compensates for the lower value of b2 compared with b1. (While x = 1 implies x2 = 1, x = 2 implies x2 = 4, and so forth.)

Figure A1. Graph of the function y = 6 + 2∙x + 0.5∙x2

Figure A2. Graph of the function y = 6 - 2∙x + 0.5∙x2

Figure A3. Graph of the function y = 6 - 2∙x - 0.5∙x2

Figure A4. Graph of the function y = 6 + 2∙x - 0.5∙x2

The regression function used in chapter 6

The regression function of the analysis presented in chapter 6 can be expressed as follows:

yi = a + b1∙xBirthyear i + b2∙xFathered 1 i + b3∙xFathered 2 i + b4∙xFathered 4 i + b5∙xFathered 5 i + b6∙xFathered 6 i + b7∙xFathered 7 i + b8∙xFathered 8 i + b9∙xMothered 1 i + b10∙xMothered 2 i + b11∙xMothered4 i + b12∙xMothered 5 i + b13∙xMothered 6 i + b14∙xMothered 7 i + b15∙xMothered 8 i + ei

Where

The father’s education reference category is ‘Lower secondary or second stage of basic’. The following variables are the father’s education dummy variable set:

Similarly, the mother’s education reference category is ‘Lower secondary or second stage of basic’. The mother’s education dummy variable set has the same categories as the father’s education dummy variable set. For example: