$Interpretation of signifcance of continous by continous regression with interaction term$

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$Interpretation of signifcance of continous by continous regression with interaction term$

Hello,
I am running a regression with a continous DP (scale of self-assesement of a person´s willingness to accept pay cuts to protect the climate) and two continous IVs (1=age 2=value-index) and their interaction.
My hypothesis is that age has a negative effect on a person´s willingness to accept said paycut and want to control it with IV2 for a person´s political values. In short: When holding values constant, does age still have the negative effect?

In Model 1, the Interaction and IV 2 are significant, while the IV 1 is not. In Model 2 only IV 2 is signficant. I have created marginplots but need some input in regard of the interpretation of the signficance in both Models.

1. Can I say that IV 1 has no significant effect on the DP in Model 1 and 2 and therefore I cannot accept my hypothesis?
2. How do I interpret an non-siginifacnt Interaction Term?
3. Is it still okay to show the plots of average marginal effects and predicitve margins for illustrative purposes and add a "non-significant but still relevant - mark"?

Here for more visual explanation

	Model 1	Model 2
Age	-0.4	-0.6
Value-Index	1.1***	1.2***
Age#Value-Index	-0.01**	-0.002

Thank you very much for any input

Regression

Ataraxon

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First: There should not be an interaction term with continuous variables. Interaction terms appear when there are indicator variables for categories, alongside a continuous independent variable.
For example:
Liberal = 0, Authoritarian = 1, Sadist = 1, Patriotic = 1

Then a regression model with interaction terms would look like:

DP = b_1 x Age + b_2 x Authoritarian + b_3 x Sadist + b_4 x Patriotic + b_0 + b_5 x (Age x Authoritarian) +... for all other interactions

The interaction term coefficients could then be interpreted as slope adjustments, compared to liberals.
The coefficients of each indicator variable indicate vertical shifts in the DP, relative to liberals.

But to answer your questions:

1. Yes, it would appear changes in Age itself does not significantly change DP, after considering factors, including 'interactions' with the Value Index. (In both models)

2. An interaction-term (with indicator variables as above) has a coefficient which represents a rate shift compared to a baseline indicator. It being non-significant just means that the sample's difference in rate between indicator variable and baseline indicator could be a result of sampling variability, and not some inherent difference as a result of the interaction/indicator variable.

3. Plots should always be included with interpretations: it could show why terms are not significant, or even why terms are significant (such as influential points/ outliers). You could also comment whether your plots meet the conditions needed for a regression analysis (e.g. normality of residuals).

Matchmaticians Alumnus

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$Interpretation of signifcance of continous by continous regression with interaction term$

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