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enter image description hereThe slope coefficient for SO2 is quite small (0.33), especially as compared to the other three slopes). Does this suggest that the effect of SO2 is therefore not very important?

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  • $\begingroup$ Please type your question as text, do not just post a photograph (see here). $\endgroup$ – gung - Reinstate Monica Mar 16 '19 at 3:15
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    $\begingroup$ Slopes are an artifact of the units used for measurements. I'd pay more attention to small P-values. Also, see Wikipedia or elsewhere for VIF. $\endgroup$ – BruceET Mar 16 '19 at 3:39
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No, it certainly does not mean this. You need to carefully consider the units of the regressors when considering marginal effects. Consider, for example, the model $$y_i=a+bx_i+\epsilon_i,$$ where $x_i$ is measuring weight of something in tons (2000 pounds per ton). $\hat{b}$ estimates the change in $y$ resulting from a one-unit change in $x_i$. If we ran the same regression with $x_i$ being rescaled to be measured in pounds (multiplying each value by 2000), our estimate of $b$ would be our original estimate divided by 2000. Both estimates imply the same marginal effect.

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    $\begingroup$ Good answer - even I could understand that one. $\endgroup$ – James Phillips Mar 16 '19 at 12:46

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