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This might be a simple question on regression analysis, but I wanted to hear your thoughts to make sure I haven’t missed anything.

Suppose I am studying the relation between ice hockey players' experience and aggressive game behavior in the rink. Say I run an OLS regression analysis with multiple independent variables. The dependent variable is total penalty minutes of an ice hockey player and the key independent variable is player tenure in a team (in months). Include several control variables. Suppose after running the regression I obtain a negative coefficient of -0.42 for the player tenure variable and the coefficient is significant at the 5% level.

Now suppose I run the exact same regression (with same control variables) but replacing the key independent variable player team-tenure with player total career experience in ice hockey (in months). Now I obtain a negative coefficient of -1.01 and the coefficient is significant at the 1% level.

My question: The coefficient of the second regression (total hockey career experience as the independent variable) is both greater in magnitude and more statistically significant than in the first regression (team tenure as the independent variable). Does this allow us to say that the total career experience is generally a stronger determinant of penalty minutes (aggressive behavior)? Or is there a reason why we cannot compare the two regressions? Would I need to conduct additional tests to make such a statement?

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The magnitude of each coefficient is directly associated with the scale of the covariate. For example, say that you want to put the age of the players as an explanatory variable. The coefficient you will obtain will have a very different magnitude depending on whether you will put age in years or hours. For this reason, sometimes you may consider scaling the explanatory variables for their standard deviation; for more info on this, check this paper by Andrew Gelman.

Related to this, it is not the strength of statistical significance that determines how "important" an explanatory variable is. This is more related to the effect size; check the discussion in this question for more info.

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  • $\begingroup$ Apologies for my delayed response. Thank you for your answer, I found it particularly helpful in directing my thinking forward. $\endgroup$
    – lambda111
    Commented Dec 6, 2018 at 15:20

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