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Consider two ways of interpreting or displaying the coefficient estimates in a regression.

  1. For a small increase in X, Y decreases by the coefficient estimate amount.

  2. For a one standard deviation larger increase in X, Y increased around some percent relative to the mean.

Which interpretation is more insightful and why?

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  • $\begingroup$ Note that if you care about interpreting coefficient estimates as measures of effect, standardized coefficients might most surely mislead you. See Greenland et al. (1986; 1991) $\endgroup$
    – Kuku
    Commented Mar 5 at 10:19
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    $\begingroup$ The "percent increase" interpretation is simply incorrect. $\endgroup$
    – whuber ♦
    Commented Mar 5 at 16:27
  • $\begingroup$ @whuber wouldn't that depend on the specification (e.g., log-linear)? it was an example and could be valid. $\endgroup$
    – Frank Swanton
    Commented Mar 7 at 17:42
  • $\begingroup$ @Frank That would be described differently: it would be a regression of $\log(Y)$ against $X.$ $\endgroup$
    – whuber ♦
    Commented Mar 7 at 19:15

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You seem to be asking whether it is more insightful to use standardized or unstandardized coefficients when interpreting regression results. Like many questions in statistics, it depends. If the goal is to understand (or predict) the precise change in $Y$ due to a specific change in $X$, than an unstandardized $\beta$ is appropriate. However, if the goal is to compare the relative importance of different variables in the model (especially when those variables are on different scales), then a standardized $\beta$, which can be interpreted in terms of standard deviations, is more appropriate.

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    $\begingroup$ See my comment on the original question regarding standardized coefficients being more appropriate to "compare the relative importance of different variables in the model". Table 2 in the Greenland et al., (1986) paper includes an example where the standardized coefficients and the population attributable fraction reverses the order of which variable has a larger effect. $\endgroup$
    – Kuku
    Commented Mar 5 at 10:22

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