Have a look at Thom's and my answer to this question

https://www.researchgate.net/post/How_to_calculate_the_effect_size_in_multiple_linear_regression_analysis

Hello Nitu,

Unstandardized regression coefficients tell you how much change in Y (the amount is B) is predicted/estimated to occur per unit change in that independent variable (X), when all other IVs are held constant. These retain the individual scales of the IVs and the DV.

Standardized regression coefficients tell you how much change in Y (the amount is the "beta", representing number of standard deviations) is predicted/estimated per unit (SD) change in that X, when all other IVs are held constant. These values pertain only when all variables are scaled to z-scores (mean = 0, SD = 1), and do not represent the original scale(s).

Comparison of relative emphasis given to individual IVs is only possible when all are on a common scale, so standardized coefficients would be the ones to look at when you are trying to determine relative weight given to each IV.

Good luck with your work.

I have a less optimistic view of standardised effect size - they don't in my view put variables on the same scale (at least not without some strong assumptions about the sample SDs).

However, as a description of a regression equation they are arithmetically and fairly trivially related to each other. For example if SD[x] is the SD of X and SD[y] is the SD of Y then in a regression of Y on X:

b = r * SD[y] / SD[x]

I really appreciate the prompt responses of academician here. Special thanks to Sir Melvyn, Sir David and Sir Thom. It really helped me to clear my doubt.

If an independent variable is expressed in millions or billions of dollars it can have unstandardized estimate close to zero. To make the coefficient value more interpretable, we can rescale the variable by dividing the variable by 1000 or 100,000 (depending on the value). After rescaling the variable, run regression analysis again including the transformed variable. You would find beta coefficient larger than the old coefficient value and significantly larger than 0.

Unstandardized coefficient should not be used to drop or rank predictors as it does not eliminate the unit of measurement

To add a bit more to my earlier reply.

Some things such as distance, temperature, income. wealth are measured on a direct meaningful scale. Then it is quite useful to know the un standardized effect- how much an extra thousand dollars of income changes the outcome. This is often very meaningful for policy.

Other types of research have variables measured on rather arbitrary scales and may come out of a factor analysis or some scoring system. In this case, the standardized coefficients may be useful as they give a change in the response in terms of 1SD change in the predictor variable.

The intercept in both types of coefficient is the value for the response when all the predictors have the value of zero. In the un-standardised case this may be outside the range of the values of the predictors, so I often center my continuous predictors around their midpoint to get a more meaningful intercept. For the standardized case the intercept applies to the mean value of all the predictors.

On intercepts see

https://www.researchgate.net/post/When_should_we_force_the_intercept_to_zero

Nitu Kaur , here is a note I wrote some time ago when reading John Fox's book on regression and GLMs. Perhaps you'll find it useful.

--------------

In his book "Applied Regression Analysis and Generalized Linear Models" (2008, Sage), John Fox is very cautious about the use of standardized regression coefficients. He gives this interesting example. When two variables are measured on the same scale (e.g.,years of education, and years of employment), then relative impact of the two can be compared directly. But suppose those two variables differ substantially in the amount of spread. In that case, comparison of the standardized regression coefficients would likely yield a very different story than comparison of the raw regression coefficients. Fox then says:

"If expressing coefficients relative to a measure of spread potentially distorts their comparison when two explanatory variables are commensurable [i.e., measured on the same scale], then why should the procedure magically allow us to compare coefficients [for variables] that are measured in different units?" (p. 95)

Good question!

A page later, Fox adds the following:

"A common misuse of standardized coefficients is to employ them to make comparisons of the effects of the same explanatory variable in two or more samples drawn from different populations. If the explanatory variable in question has different spreads in these samples, then spurious differences between coefficients may result, even when _unstandardized_ coefficients are similar; on the other hand, differences in unstandardized coefficients can be masked by compensating differences in dispersion." (p. 96)

And finally, this comment on whether or not Y has to be standardized:

"The usual practice standardizes the response variable as well, but this is an inessential element of the computation of standardized coefficients, because the _relative_ size of the slope coefficients does not change when Y is rescaled." (p. 95)

When regression co-efficiant 1.0 ) the method is insignificant .

Linear Regression : Unstandardized Coefficient

It represents the amount by which dependent variable changes if we change independent variable by one unit keeping other independent variables constant.

Linear Regression : Standardized Coefficient

The standardized coefficient is measured in units of standard deviation. A beta value of 1.25 indicates that a change of one standard deviation in the independent variable results in a 1.25 standard deviations increase in the dependent variable.

The standardized coefficient is found by multiplying the unstandardized coefficient by the ratio of the standard deviations of the independent variable and dependent variable.

Ranges: When regression co-efficient values 1.0 ) the method is insignificant .

Hello David Morse, thank you for your answer. In most cases it is not possible to standardise the DV because it is a counter which is used as outcome in a Negative Binomial Regression model. However, the standarization of IVs might be helpful for the regression problem as they could be in different scales. In this case, where IVs are standardised but the DV are not, it is possible to give an interpretation to regression coefficients? If so, what is it? Thank you very much

Hello Gabriele Accarino ,

I just noticed this post of yours. In a dichotomous DV model (whether logistic, negative binomial, or other), standardizing the IVs would allow you to make judgments of relative emphasis being given to IVs by comparing the regression coefficients. If that is helpful, you can always give it a try.

Even though standardized scores are just a linear transformation of the original scale, they sometimes make folks uncomfortable in straying away from the metric with which they are more familiar.

Good luck with your work.

Thanks Prof. David. I am really thankful to you