1. ## Hypothesis interpretation

Dear

I'm wondering how I should interpret my hypotheses.
The first one is "the relationship between X1 and Y increases as X3 increases" and the second one is exactly the same but with X2, so "the relationship between X2 and Y increases as X3 increases"

I have used a regression analysis with the models:
Y = β0 + β1X1 + β2X3 + β3X1*X3
Y = β0 + β1X2 + β2X3 + β3X2*X3

However by doing the analysis in SPSS the significance for the first hypothesis is p=0.682 and p=0.934 for the second (This was after centering the variables to counter collinearity and coding X3 into a continious variable. It was a categorical variable before.).

All of this was done after asking a professor from the university. Still I'm wondering if this means the relationship between X1/X2 and Y declines when X3 increases? How should I interpret this? Am I using the right method?

I also have a third hypothesis about which X (X1 or X2) has the greatest influence on Y. How could I analyse this? Could I use a Shapley Owen Decomposition or eta-squared? Or is there an easier method?

Kind regards

2. ## Re: Hypothesis interpretation

Is there a reason why you cannot formulate a single regression model: Y = b0 + b1X1 + b2X2 + b3X3 + b4X1*X3 + b5X2*X3 ??

It, ostensibly, would seem to me, to be much easier to work with - statistically speaking.

3. ## Re: Hypothesis interpretation

Originally Posted by Dragan
Is there a reason why you cannot formulate a single regression model: Y = b0 + b1X1 + b2X2 + b3X3 + b4X1*X3 + b5X2*X3 ??

It, ostensibly, would seem to me, to be much easier to work with - statistically speaking.
I used 2 models because of the 2 different hypotheses. I could use a single regression model like you mentioned and then p=0.984 for X1*X3 and p=0.738 for X2*X3.
How should I interpret these?

4. ## Re: Hypothesis interpretation

Originally Posted by Hypnoz
I used 2 models because of the 2 different hypotheses. I could use a single regression model like you mentioned and then p=0.984 for X1*X3 and p=0.738 for X2*X3.
How should I interpret these?
Easy, get rid of the interaction terms and use the model with the just main effects i.e., Y, X1, X2, X3.

5. ## Re: Hypothesis interpretation

Originally Posted by Dragan
Easy, get rid of the interaction terms and use the model with the just main effects i.e., Y, X1, X2, X3.
This allows me to see the influence of X1 and X2 on Y when X3 increases?
How would you do the third hypothesis?

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