Results in Mathematics and per capita GDP
Per capita GDP
Figure 1: P.GDP and the results in Mathematics in PISA 2012. Lines are
polynomial estimators of the regression of the scores on the logarithm of the
P.GDP. Liechtenstein, Qatar and Vietnam are denoted as Lie, Qat and Vie
Country P.GDP log
. . .
2 Liechtenstein 89,400
58 Thailand 9,875
3 Luxembourg 78,670
59 Albania 9,506
4 Singapore 64,584
60 Jordan 6,115
61 Indonesia 5,214
. . .
62 Vietnam 4,012
Table 2: Five highest and lowest P.GDP’s and their logarithms of the countries
participating in PISA 2012.
should not damage the score. Even if there exist techniques which allow to
under shape restrictions (some references on those techniques are
Barlow et al., 1972, and Robertson et al., 1988), here, I have decided to skip this
I have handled two possibilities for the regression function: Firstly I have
assumed that the function
is a polynomial. Secondly I have made no
and I have used a so-called non-parametric estimation of
Both possibilities are analyzed in the next two subsections.
Some theoretical development on polynomial regression can be found in
Draper & Smith (1998) or Sen & Srivastava (2011).