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3

But I do not understand what it means by "correct test for significance". Can someone explain what he's referring to? If I were you I would post a comment to that answer by @EdM, otherwise, unless they actually see this question and answers themself, we can only make an informed guess. Having said that, what I think is meant by that statement, is that the ...

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In the first model, the coefficient on $X_2$ (i.e., $b_3$) corresponds to the expected slope of $X_2$ on $Y$ when $X_1=0$. Omitting this term as in the second model is essentially forcing the coefficient on $X_2$ to be equal to zero. If that coefficient is indeed zero in the population, then there is no harm in setting it to zero, but typically researchers ...

3

The main effects in a model that includes an interaction have a different meaning than in a model that does not include an interaction. Without an interaction, a main effect can be interpreted as the association of a 1 unit change (or of the difference with respect to the reference level with a categorical variable) with the response/outcome variable, ...

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Most statisticians will tell you that categorizing a continuous variable is a bad idea, and I generally agree with that. In your case, you can allow the effect of continuous x to vary by a person's gender. This would then induce separate slopes of x for males and females as well as intercept values for males and females at x==0. It preserves all the ...

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The basic option, as in the effects package is to plot fitted values against one of the interacting regressors while fixing the other regressor at a representative value (say, mean, median or any "interesting" value). For effects package syntax and examples, see https://cran.r-project.org/web/packages/sjPlot/vignettes/plot_interactions.html Alternatively, ...

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The interaction term you propose would give you a predictor that is 0 for values of $x$ less than or equal to 0.5 and equal to $x$ for values above that. In principle there's nothing wrong with that formulation of a predictor variable in your regression. That wouldn't, however, test your hypothesis that "$x$ is a significant predictor of $y$ but only when $... 0 Multiple regression model always capture effect et ceteris paribus for each variable, meaning when every other variables are held constant. I think this property is enough to justify my first intuition, that is: In Equation$(1)$:$\hat{\beta_a}$accounts for$e_1 + e_2$In Equation$(2)$:$\hat{\beta_a}$accounts only for$e_2$;$\hat{\beta_b}\$ accounts ...

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Regarding p-values: The p-values in the regression output are used to test the null hypothesis that the regression coefficient is 0, or in other words, that the variable is useful in predicting the response, given that the other variables are in the model. So the fact that the p-value for Time:Diet2 is greater than 0.05 means that you can conclude the ...

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To see if there is a statistically significant interaction, you need to inspect the p-values, and sizes, for the estimated interaction(s). In R you can obtain these from > summary(model) An interaction occurs when the estimates for a variable change at different values of another variable, and here "variable" could also be another interaction. anova(...

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I've made a few example models which should be nested if you just test them in order. The model I believe best is chickm6 which: removes the baseline Time 0 Diet effect, which is intuitive since at Time 0 (I would imagine at birth), the Diet should not have any effect on chick weight added a linear two-piece spline, with the knot placed at Time 6 (somewhat ...

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A couple of points: These models are nested and therefore you can also use formal hypothesis testing using F-test to compare them. These F-test are provided by the lmerTest package. In general it is not good to only look at measures like AIC or p-values to decide which terms to include in the model, especially the fixed effects in this case. You should also ...

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