# 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∙x^{2}. 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∙x^{2}. 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 b_{2} compared with b_{1}. (While x = 1 implies x^{2} = 1, x = 2 implies x^{2} = 4, and so forth.)

Figure A1. Graph of the function y = 6 + 2∙x + 0.5∙x^{2}

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

Figure A3. Graph of the function y = 6 - 2∙x - 0.5∙x^{2}

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

## The regression function used in chapter 6

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

y_{i} = a + b_{1}∙x_{Birthyear i} + b_{2}∙x_{Fathered 1 i} + b_{3}∙x_{Fathered 2 i} + b_{4}∙x_{Fathered 4 i} + b_{5}∙x_{Fathered 5 i} + b_{6}∙x_{Fathered 6 i} + b_{7}∙x_{Fathered 7 i }+ b_{8}∙x_{Fathered 8 i} + b_{9}∙x_{Mothered 1 i} + b_{10}∙x_{Mothered 2 i} + b_{11}∙x_{Mothered4 i} + b_{12}∙x_{Mothered 5 i} + b_{13}∙x_{Mothered 6 i} + b_{14}∙x_{Mothered 7 i} + b_{15}∙x_{Mothered 8 i} + e_{i}

Where

- y
_{i}is person i’s education length - x
_{Birthyear}i is person i’s birth year

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:

- x
_{Fathered 1 i}has value 1 if i’s father has not completed an education, and value 0 if he has - x
_{Fathered 2 i}has value 1 if i’s father’s highest education is primary or first stage of basic, and value 0 if it is not - x
_{Fathered 4 i}has value 1 if i’s father’s highest education is upper secondary, and value 0 if it is not - x
_{Fathered 5 i}has value 1 if i’s father’s highest education is post-secondary, non-tertiary, and value 0 if it is not - x
_{Fathered 6 i}has value 1 if i’s father’s highest education is first stage of tertiary, and value 0 if it is not - x
_{Fathered 7 i}has value 1 if i’s father’s highest education is second stage of tertiary, and value 0 if it is not - x
_{Fathered 8 i}has value 1 if i’s father’s highest education is unknown, and value 0 if it is not

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:

- X
_{Mothered 1 i}has value 1 if i’s mother has not completed an education, and value 0 if she has And so forth.