You can add an interaction term to regression model and test its significance.
Mehmet, if you look at the sample sizes you will notice that they are not equal, so it seems that the response is measured independently for both predictors. If this is the case then I do not understand how one can calculate an interaction.
AIf I am right, then one can only roughly estimate the significance employing error-propagation:
The standard errors of the coefficients (slopes) must be known. The standard error of the difference can then be estimated as the sqare root of the sum of the squared standard errors. The ratio of the difference of the slopes (3.14-2.12) dvided by its standard error is a t-statistic. Having rather large sample sizes (and knowing that we anyway work only on a rough estimate) this can be taken as a z-statistic, so the significance can be calculated from the standard normal distribution.
No you can calculate interaction as that variable of interest (whose regression slope is known) multiplied by group indicator. And the significance of that interaction term gives you equality of slopes.
Mehmet, I did not understand your solution. Could you possibly show practically how to get the interaction (including its standard error or confidence interval or p-value). You may use the data I attached.
I think Mehmet is suggesting something like this (?) :
> anova(lm(y~Exp*x,data=JochenTable))
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
Exp 1 1712650 1712650 186.4071 < 2.2e-16 ***
x 1 3720 3720 0.4049 0.5275
Exp:x 1 707546 707546 77.0103 1.277e-11 ***
Residuals 49 450197 9188
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
with this kind of table :
Exp x y
Exp1 174 52.95289897
Exp1 934 363.4672704
Exp1 3 112.5821122
... ... ...
Exp2 324 771.0225659
Exp2 264 694.4829434
Exp2 482 439.1368907
Regards
Freaky, yes - where was my brain?! That was a clear black-out.
Thank you, both of you!
And shame on me!
Yes you were right. I did not see this.
To my excuse I was in a problem where the x-values were quite different (not in the same range) between the experiments (not like in the fake data I attached!), so the interaction would refer to an extrapolation for both experiments. This would still be ok when the linear relationship is ok even at x-values outside of the measured ranges... but my brain told me that there must be some problem.
Also, the problem remains when the response (y) or the predictors (x) are not the same in both experiments (like - to be crude - a distance in exp.1 and a time in exp.2). There was no information in the original question about the similarity of the two data sets. So I still make the point that it might no be possible to calculate any meaningful interaction.
Sorry for the confusion, and thank you again for clarification!
Yes we are speculating about the issue as mostly done in some RG threads.
Sometimes I feel like I am being scammed, because after giving the answer no replies return from the poster . And moreover people began a hard discussion about the issue without any vital signs from the original poster which is being sometimes funny.
I also recognize this but I don't feel too negative about that. Sure, discussions only about what the questioner might have meant are clearly a waste of time, though. But often, questions are simply initiating good discussions from which I learn a lot, and this sometimes happens just because the question or the problem is not entirely clear.
Thank you very much!!!
Your coments were really helpful!
I repeated step by step as you adviced
and it works !!!!
Best regards,
Tata
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