OLS Model: Diagnostics
We chose the OLS model based on the results of 5 tests: linearity, normality, homeskedasticity, independence, and multicollinearity. The results of each test is shown below.
Linearity
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Normality
- The Kernel density shows that the error is normally distributed, proving normality.
- The pnorm is sensitive to non-normality in the middle range of data, but it is not apparent in this graph, showing no indication of non-normality.
- The qnorm is sensitive to non-normality near the tails. This graph shows a slight deviation from normal at both tails.
Homoscedasticity
Independence
PISA data comes from 1367 different schools. OLS regression assumes that the residuals are independent, so we ran a regression with clustering the different schools together. The observations may be correlated within each school, but would be independent between districts. The coefficients that were significant in the OLS analysis are significant in this analysis as well.
Multicollinearity