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Univariate analyses were performed to describe the relationship between each explanatory variable and the outcomes.
A bivariate analysis was conducted to determine the association between each explanatory variable and HL outcome.
Associations between each explanatory variable and current smoking were measured by Pearson's χ test with a p value <0.05.
R-squared partial correlations were used to measure the marginal contribution of each explanatory variable when all others were already included in the model.
This process results in the estimation of the independent contribution of each explanatory variable (Ii), and the joint contribution (Ji) resulting from correlation with other variables [ 50].
Unadjusted results consider the association between the outcome and each explanatory variable individually.
Associations between the outcome variable (abstinence) and each explanatory variable were investigated using chi-square test.
This means that finding a correlation between the explanatory variable and the dependent variable is made harder and thus, when such a correlation is found, it can be interpreted as strong evidence of its existence.
Thus, to avoid any confounds due to multicollinearity (correlation between two explanatory variables), we ran each term in a separate model.
Estimating using a Hausman–Taylor model to control for the possible correlation between our explanatory variables and unobservable university-level effects, we find that the fees charged may influence the application decision of some students, but that any relationship between levels of fees and applications is non-linear.
To avoid correlation between the explanatory variables, a principal component analysis (PCA) was applied on the correlation matrix of climatic and elevation variables.
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