# Scaling odds ratios and converting them to probability

I'm trying to calculate a scaled odds ratio and convert them into percentages for an analysis I am doing.

I have just one independent variable in the model, SAT score. Dependent variable is college acceptance. The SAT score is in 1-point increments, so odds ratio calculated was for 1-point change.

However, I want to make this into something more interpretable in real life. The odds ratio for 1-point change in SAT score was 1.08.

How do I calculate the odds ratio for 10-point or 25-point increase in SAT score? My understanding is just raising OR to the power of the point increase, i.e. 1.08^10 and 1.08^25.

Can I convert the odds ratio into percent change in college acceptance for a 10 or 25-point increase in SAT score?

Thank you.

From your question, I assume you have the following logistic model: $$\mathrm{logit}(\texttt{Acceptance})=\beta_0 + \beta_1\texttt{SAT_score}$$
The odds ratio for one unit increase in $$\texttt{SAT_score}$$ is $$\exp(\beta_1)$$, where $$\beta_1$$ is the coefficient for $$\texttt{SAT_score}$$ on the log-odds scale. The odds ratio for $$u$$ units increase in $$\texttt{SAT_score}$$ is $$\exp(\beta_1\cdot u)$$. So for $$u=10$$ or $$u=25$$, you have $$\operatorname{OR}_{10}=\exp(10\beta_1)$$ and $$\operatorname{OR}_{25}=\exp(25\beta_1)$$.