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This link may be helpful for you: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-do-i-interpret-odds-ratios-in-logistic-regression/ Typically, odds ratios are interpreted as scalars that represent the increased/decreased likelihood of association to the response variable. For example, if this GLM was from a logistic family, we could say that,...

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It's saying that the odds of females graduating is 4.31 higher than the odds of males, holding constant disorder. That doesn't mean females are 4.31 times more likely to graduate, but it does mean females are more likely to graduate. You can think of it as that among females, the ratio of the number who graduate to the number who don't graduate is 4.31 times ...

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The intercept is the log of the odds of 'success' (i.e., that $Y=1$) when all the regressors are equal to $0$. If you exponentiate the intercept, you get ${\rm odds}(Y=1|X=0)$. This is often not of substantive interest in a study, but it is a necessary part of the model.

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You don't really give enough information for anyone to give a complete answer, but a skim of the paper and your question leads me to suggest using the interaction test approach in your regression model(s). That is, you add an interaction or product variable between your grouping variable and the exposure variable of interest. The null hypothesis for this ...

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Your coefficients (or more specifically, the exponentiation of your coefficients) are the ratios of the odds at X and X+1, or the ratio of odds per unit change of the predictor variable. Mathematically, $\frac{Odds(Y=1|X=x+1)} {Odds(Y=1|X=x )}=e^{\beta_i}$

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$\newcommand{\op}[1]{\operatorname{#1}}$ Let's use some abbreviations as follows: \begin{align*} \op{UTRS}&=\text{Upper Trunk Rotation Strength}\\ \op{I}&=\text{injuries}\\ \op{A}&=\text{Age}\\ \op{W}&=\text{Weight}\\ \op{PCS}&=\text{Posterior Chain Strength}\\ \op{GS}&=\text{General Strength}. \end{align*} Now the basic model under ...

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