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I'm currently a high school senior working on an astronomy research project, and am having trouble determining if there's a special kind of statistical analysis that I need to perform on my data.

I'm looking at the relationship between a stellar attribute (luminosity) and a planetary attribute (radius) in hot jupiter exoplanets. I took data from the NASA Exoplanet Archive for this analysis. My preliminary analyses found a significant positive trendline between the two.

However, I wanted to see if this trendline held with different star ages. So I sorted my data into nine age ranges, and did the same analysis for each of those groups. This gives me a total of nine slope values and nine r^2 values, one for each age range. I want to see if there's any statistical variance between the slopes and r^2 values of the different age ranges, and if there's a trend to those values as age increases.

What I've done so far is graphed the values in bar graphs, with the independent variable being the age range, and the dependent variable being the slope or r^2 value. I've looked at the slope and r^2 of the trendline of that graph to tell me if the amount of significant effect on the planet changes as stellar age increases.

However, I don't know if that's enough, and if there's a more rigorous statistical test that I should be doing. Is there any kind of test specifically for analyzing the significance of the trendlines different groups, and looking for a correlation between group and significance? Is the analysis I'm doing already enough for my level?

I apologize; statistics isn't my strong suit, and I don't know if this is the best place to ask. But I appreciate any help and suggestions anyone has.

The Bookwyrm
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    Using $R^2$ can be very misleading and is difficult to interpret: see the example at https://stats.stackexchange.com/a/13317/919. Sorting a variable into nine groups looks arbitrary and it also loses information. It sounds like you need some form of [tag:multiple-regression]. – whuber Feb 23 '24 at 21:38
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    There is a standard statistical procedure for the scenario of a continuous outcome (radius) with one continuous (luminosity) and one discrete predictor (binned age): one-way ANCOVA.

    But I second @whuber's warning that binning one of your predictors seems arbitrary. If your goal is inference, it would be better to start by fitting a multiple linear regression without first tinkering with the predictors.

     – jdonland Feb 24 '24 at 20:38

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