OLS regression, student level: Math achievement on liking math and cultural values

Here’s a description of the project I’m working on.

I duplicated all country-level variables to student level, then ran a student level regression of math on liking for math (PATM), per capita GDP (GDP), and cultural value indexes (Rational and Self Expressive).

Collinearity was not too high — all variance inflation factors were less than 3.

Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
(Constant) 382.428 .586 652.822 .000
PATM 4.969 .066 .163 75.521 .000
GDP 4.787 .027 .592 175.670 .000
Rational 23.244 .249 .235 93.291 .000
Self Expressive -33.841 .279 -.361 -121.273 .000
a. Dependent Variable: Math

These are all as I expected.

  • The more a student likes math, the better she does (this is a reciprocal relationship because if you do better at math, you like it better too)
  • Higher GDP is associated with higher math achievement
  • Higher secular rational values are associated with higher math achievement; in other words, traditional values are associated with lower math achievement
  • Higher self expressive values are associated with lower math achievement

The residuals looked fairly normal, though there were more positive ones than negative ones.This could represent an omitted variable (perhaps extrinsic valuing of math? which I could calculate from some other TIMSS questionnaire items) or some nonlinearity in the relationship.

The model has an R square of .321.

Now I’m ready to start running HLM analyses to see if countries with higher rationality and lower self expressiveness offer higher “returns” to liking math.