First, let’s try to transform Ozone concentration as hinted in the description and see if the model performance regarding to significance improves. We start by taking the square and the cube transform of the dependent variable but we see that on taking higher powers of the dependent variable, the adjusted R-squared value decreases from 0.557 to 0.4316 which signals that taking higher powers of the dependent variable might not be the right approach. A summary of these models along with some visual representation is present in the appendix.
We move on to working with the logarithmic and root transforms of the dependent variable. We see that on taking the log transform of the dependent variable, the adjusted R-squared increases to 0.695 and we observe that for this linear model, temperature and inversion height are significant explanatory variables.
We move to the square root transform of the dependent variable and see that the adjusted R-squared increases upto 0.7147 and inversion temperature joins the list of statistically significant explanatory variables. There are still numerous insignificant explanatory variables because of the high correlations that we had observed earlier but since the model seems to improving with decreasing function transformations on the dependent variable, we try the cube root and the fourth root transformations as well. We judge the performance of the model by improvements in the adjusted R-squared values and whether make explanatory variables become significant. We see that beyond the cube root of the dependent variable, we do not get any further improvements in the model, therefore we now start looking at interactions. The summary tables for all the models stated above as well as the summary plots can be found in the appendix.