Regression with sqrt transformed dependent variable - meaning of the model's B value?

#1
Hi fellow nerds :)

My dependent variable had to be transformed by square root (so the residual plot would be normal).

I usually use log10 transformations and then the B value (slope) translates into the percents of the dependent variable, but what do I read from a B=-,499 (P=0,015) of a sqrt transformed dependent varible (insulin in blood)?

I hope someone who was once as stupid as I am in stats understand the question and is willing to help ;) English is not my native language so I am sorry if I put some annoying errors in the text.
 
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#2
Re: Regression with sqrt transformed dependent variable - meaning of the model's B va

The coefficient in that context would just mean that a one unit change in \(x_k\) is associated with a change of \(\beta_k\) in \(\sqrt{y}\). There's not a lot of intuition there.

Is there some reason why you're choosing to transform the dependent variable instead of one or more of the indepdent variables? I would suggest including a quadratic in the offending independent variables, instead. Those betas will have a much more intuitive and valuable interpretation.
 
#3
Re: Regression with sqrt transformed dependent variable - meaning of the model's B va

The Xk used by the first reply was because the author was assuming you had more than one independent variable, in which case Xk refers to the particular independent variable whose effect on Sqrt(y) is estimated as B = -0.499 in your analysis. To make matters simple for you, I am assuming you had only one independent variable X and one dependent variable y which you transformed to Sqrt(y) . From now on, we talk about X instead of Xk The computational system you used to analyse the data did not only calculate B which we call “an estimate of the regression parameter”, it went ahead to test if the actual (population) B is effectively zero or not, on the basis of sample data. (Remember you calculated B from sample data instead of data representing the entire population. Hence it is possible for B in the population to be 0 but B calculated from a sample taken from the population is not 0). If B is effectively 0, it means that there is no meaningful regression between X and Sqrt(y). Regression is a mathematical expression of relationship between two or more variables, in your case, x and Sqrt(y). And this relationship is expressed in its simplest form as Sqrt(y) = A + BX If the test shows that B is effectively 0, then there is no effective relationship between X and Sqrt(y).
By showing (P=0,015) the computational system has tested the claim “B is effectively 0” and given judgment which is “The P-value of 0.015 is less than 0.05, therefore B is not equal to 0”. In statistical jargon, we say that the test is significant. Now, if the P-value was 0.13 which is greater than 0.05, then B is effectively 0 and the test is not significant. The role of 0.05 (otherwise called 5% level of significance) here is that of a benchmark for making the statistical decision. It also represents the chance that the test could be erroneous. Recall you are working with a sample and not the entire population. Suppose you wanted to minimize chance of erroneous test to 1% , then the significance level of the test would be 0.01. You can verify that a significance level of 0.01 would have led to a different conclusion about B.
From: oparairoegbu, Lagos, Nigeria.
 
#4
Re: Regression with sqrt transformed dependent variable - meaning of the model's B va

Thank you both for your answers :) (and yes I have only one dependent variable in this case).