Significance of constant - Mean adjusted values vs. Z scores

Hello everyone,

I am trying to run a regression analysis on 2 Inputs and their relationship with 1 Outcome variable across a number of products. I have multiple observations per product, and tried in two ways to make the data comparable in magnitude between products. One is a mean adjust (divide each input & outcome value by the mean of that variable for that product) and z Scores.

I get different results for the significance of the constant in the model and I am not sure why.

Mean adjust result:
0.982 (constant) + 0.079 * Input 1 - 0.061 * Input 2 = Outcome
Both the constant and both coefficients are significant to 0.000.

Z Score result:
0.00000000000000045409 (constant) + 0.692 * Input 1 - 0.476 * Input 2 = Outcome
Now the constant comes back with significance 1.000 and both coefficients are still significant to 0.000.

If I understand it correctly, 0.000 means that we should reject null hypothesis and accept the alternate hypothesis, both coefficients add a meaningful amount to the model. What I don't understand is why in the Z score run, the constant is not significant. Is it because it is (practically) zero? If it makes any difference, I am using SPSS.

Re: Significance of constant - Mean adjusted values vs. Z scores

Hi all,

I think I figured it out. Seems to have been a case of "not seeing the forest because of all the trees"...

If I understand it right, it just means the constant is not significantly different from zero, which is obvious as it is practically zero - and this is driven by the fact that the Z score adjustment automatically centers the data around zero.

Would be great if someone could let me know if I'm still not getting it

Re: Significance of constant - Mean adjusted values vs. Z scores

You are right about what happens when you do these two analyses.

However, if you have multiple observations per product, you may want a multilevel model; it's hard to tell from what you posted, but you may be violating the assumption of independent errors

Re: Significance of constant - Mean adjusted values vs. Z scores

Hi Peter,

Thanks for your comments.

I do have multiple observations per product. Ideally, I would want to run this regression at product level, but as I only have a max of 15 observations per product, I thought about using z Scores and considering all products together instead. The observations are at different points in time, but for now I am not looking at time - I know that time does matter, but for now I am wanting to focus only on the two predictors that are of concern.

I must admit I am still quite new to statistical analysis. I have not previously used a multilevel model and don't have experience with it - could you point me to any resources which may have an example? I had a look at wikipedia and also youtube, but for now it's not totally clear to me. Do you mean a hierarchical model, where I would e.g. first run the regression with only variable one, and then with add variable two and evaluate the r squared change?

On your second comment regarding the potential violation of the underlying assumption of independent errors - could you elaborate on this? I am not sure how I could test for it.

Thanks again for your thoughts, really appreciate it!

Re: Significance of constant - Mean adjusted values vs. Z scores

Sorry for the double-post. I was thinking about the independent errors part of your comment Peter. Did you mean that I should test for homogeneity of errors? I have performed the Breusch - Pagan test now and based on the results I do not reject H0 of homogeneity. I have also looked at the Durbin Watson and it is 1.507, so just about within the usual range of 1.5 - 2.5. So I would say the assumption of error independence is also satisfied.

Does this address your concern, or could you give me more details on what I am doing wrong?

Last edited by Londoner; 12-02-2014 at 10:29 PM.
Reason: details on DW