Correlation Matrix
We used a correlation matrix to analyse the relationship between PM10 and PM2.5 levels and happiness measured across England. This helped to provide a general context before we analysed the relationship at a regional scale.
Correlation matrix for the year 2011 between PM10, Happiness and PM2.5 data.
The slightly negative correlation between PM10 and happiness and PM2.5 and happiness (-0.11 and -0.12, respectively), indicates that there is a negative relationship between pollution and happiness within the datasets used. The 0.93 correlation between PM10 and PM2.5 levels in 2011 shows a positive relationship between the pollution indicators. Although it is a significant amount of correlation, causation cannot be inferred.
Correlation matrix for the year 2021 between PM10, Happiness and PM2.5 data.
Results were similar for the year 2021 with a positive correlation of 0.94 between PM10 and PM2.5 levels. Furthermore, to test for multicollinearity-- when "two or more predictors in a regression model are moderately or highly correlated to one another" (Penn State A, n.d.), a Variance Inflation Factor should be used in the future.
This would enable the assessment of "variance inflation of the coefficients" (Penn State B, n.d.) to determine whether the multicollinearity, if present, is "structural or data-based" (Penn State A, n.d.). In this case, it is more likely to be structural-- the "creation of a new predictor from other predictors" (ibid.) - as PM10 concentrations are likely to include measures of PM matter below 2.5 μm.