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I have a multiple regression equation that reads as follows:

ln10(DV) = 0.437 + 0.394(ln10(IV_1)) + 0.061(IV_2) - 0.145(IV_3)

I performed the ln10 transformations for the DV and for IV_1 to get around heavy skewness in the original data. The ln10 transformed data is normally distributed.

IV_2 is a principal component (which hasn't been transformed)

IV_3 is a variable that represents 0 = "disagree" and 1 = "agree"

The ln10 transformation helped me to perform the regression but I'm now struggling to interpret what this means in practical terms, all help appreciated!

(The model is significant, but has a fairly modest R^2 of .33)

Sam Leak
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  • Should I multiply everything by 2.303?

    log10(DV) = 0.437 + 0.394(log10(IV_1)) + 0.061(IV_2) - 0.145(IV_3)

    [IV_1 is log10 transformed, IV_2 is an untransformed principal component, IV_3 is the dummy variable)

    becomes

    ln(DV) = 1.006 + 0.907(ln(IV_1)) + 0.140(IV_2 * 2.303) - 0.333(IV_3 * 2.303)

    Then

    • For IV_2 and IV_3. Exponentiate the coefficient, subtract one from this number, and multiply by 100. Interpret the DV in terms of percentages. • For IV_1, interpret the coefficient as the percent increase in the dependent variable for every 1% increase in the independent variable.

     – Sam Leak Apr 09 '21 at 08:01
  • Also to remove zeros prior to the log10 transformations, in both instances (DV & IV_1) I added 1 to everything. How does this impact my interpretation?

    And finally, what does the R^2 value mean when the model is predicting a ln10 DV?

     – Sam Leak Apr 09 '21 at 08:02
  • Only the distribution of the residuals matters (see: What if residuals are normally distributed, but y is not?), not the marginal distribution of Y, & certainly not the distribution of any X variable. – gung - Reinstate Monica Apr 09 '21 at 14:18
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    I think you will find the information you need in the linked thread. Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. – gung - Reinstate Monica Apr 09 '21 at 14:20

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