Can you help me interpret this

[Salma Aboelmaaty]

Dear All

Looking at the below simple regression .. Can we interpret from the coefficient that independant variable (PSM) has more impact on the dependent variable (Gmotivated) than Paysatisfied? Noting that when I ran correlations, pay satisfaction had higher association with Gmotivated but in the regression, it has smaller co-efficient. What does that mean?

These are just rough examples I am providing to help me interpret the differences because I am confused between the meaning of co-efficients in both models and I feel that they are contradicting

[Clyde Schechter]

What does that mean?

It doesn't mean anything.

Regression coefficients are sensitive to the scale and measurement units of the variables involved. Unless PSMTOTAL and PAYSATISFIED are measured on the same scale and have the same distribution in that scale, it is meaningless to compare their coefficients and attempt to say that one is more related to the GMOTIVATED than the other.

The correlation coefficients are more suitable for this kind of comparison because the correlation coefficient is not sensitive to scale/measurement units. Actually, unless the two variables, when both standardized, have the same distribution, it is still not strictly correct to say that one is more strongly related to GMOTIVATED than the other, but the worst of the problems with that statement are overcome and many people will accept that conclusion.

[Salma Aboelmaaty]

Thank you so much as usual for your very helpful explanations.

But then what does the regression tell us about the relationship between the three variables? Does it just prove that both PSMtotal and PAYSATISFIED have impact on motivation at a significant level? I have two hypothesis, that PAYSATISFIED in general is more important for motivation and then the other hypothesis is that PSMtotal have actual impact on motivation. Is it then safe to use correlations to compare between the relationship of PSMtotal and PAYSATISFIED and Gmotivatied, and then afterwards use regression to see if PSM have actual impact on Gmotivated? and then it wouldnt matter that the co-efficients have been reversed? or is correlation enough to answer both questions since PSMtotal is already also correlated at a medium level to Gmotivated

Also, does it make it better to add control variables to the regression? what can constitute as an acceptable control variable other than age and gender, for example, I have variables that are related to job type, grade, and sector. Do these constitute as control variables that can be added to the regression?

[Clyde Schechter]

Importance is not a statistical characteristic of a variable and it cannot be estimated statistically. Even if PSMTOTAL and PAYSATISFIED did have the same scale and distribution, so that you might say that one is more strongly associated with GMOTIVATED than the other, you still could not say that that one is more important than the other. For example, if the more strongly associated variable is not one that can be modified through interventions, but the other can be readily manipulated, then it might make more sense to say that the more strongly associated variable is actually less important. Judgments about importance depend on the details of context. Attempting to answer such questions just through statistics are doomed to fail. Don't waste your time trying.

Most people will accept a conclusion that a variable with a higher correlation to the outcome is more strongly associated with that outcome (though, as I have said, strictly speaking this is not the case--and I haven't even approached the issue of, all else equal, is it the case that a unit difference in PSM is actually equivalent in some real world sense to a unit difference in PAYSATISFIED). That's about as far as you can take it. Why do we do regressions? Sometimes we want to predict an outcome variable from the independent variables: you can't do that with just correlations. Often we are interested in estimating the marginal effect of an independent variable on the outcome, that is, how much difference in the outcome is expected per unit change in the predictor variables. This is a more refined approach than just testing whether there is a "statistically significant" relationship.

Also, does it make it better to add control variables to the regression?

Well, it won't help you answer unanswerable questions like "which is more important." Deciding whether to add covariates ("control variables") to a model, and, if so, which ones, is a complicated topic that cannot be reviewed in a post here. And beyond the general statistical principles that apply to this, ultimately the main issues that arise deal with the subject matter you are studying, so if you are not sure what variables make sense for this role, you will need advice from somebody with a deeper knowledge of your field. To see a brief summary of the statistical principles involved, look at #6 in https://www.statalist.org/forums/for...ure-or-success.