# How can I use this data to make a function? [closed]

I'm currently in high school biology (final year) and am currently working on an assignment. I need to create some sort of interactive model, so I've decided to make a simulation-type program.

I've looked a bunch at lots of papers and journals and I was wondering how I could take the data and make a function out of it.

Here is one example (Pleasants & Oberhauser, 2012): In particular, I want to know how to make sense of the values F_1,11; r^2; and P. I am finding a lot of these values in the papers I'm looking at so it would be awesome if one of you guys could point me in the right direction.

Thanks!

• This is not really related to biology more like mathematics. The values you're interested in come from statistical tests, in your case linear regression that is indicated in the last line under the image. You should check math and statistical books for these. – Nandor Poka Apr 4 '15 at 16:39
• Thanks for the advice. I thought posting under biology would be better than math because the function could be specific to biology? Clearly, my knowledge in this is pretty thin so thanks for pointing me in the right direction. – Dillon Chan Apr 4 '15 at 18:19
• @poka.nandor yes this question is about statistics but those measures are so often used in biology that I consider them "part of the job". – cagliari2005 Apr 5 '15 at 0:48
• I'm voting to close this question as off-topic because it is about statistics. CrossValidated.SE would be a better fit. – Remi.b Apr 5 '15 at 5:14
• I think it will likely get shut down on cross validated because it's about basics - open an introductory statistics book/ Web page/ Youtube video and you'll be able to get an answer, then if you're stuck ask about specifics on cross validated – rg255 Apr 5 '15 at 7:16

I will not go too deep into the details but here some information to facilitate your understanding of these ubiquitous statistics in biology.

The F, $r^2$ and p-value are all equivalent statistics to measures the goodness-of-fit of a model against the data.

The F is the ratio of the $unexplained~variance~/~explained~variance$. I let you look out what the variance is. The F (originating from a F-test) allows, using the proper F-distribution cumulative density function (cdf) for the number of observation you have, to compute a p-value.

The p-value gives you the probability of obtaining the observed fit with your model (here a linear one) by random chance only. For example in your case a p-value=0.01 means that you have a 1% chance to observe this correlation just by chance. Usually the p-value threshold used to claim statistical significance is 0.05 (i.e. 5% chances to observe that fitting by random chance). In linear regression, the lowest the p-value the closest the distance (called variance) of the observed data point to the line.

The $r^2$ is the coefficient of determination (or the square of the correlation coefficient). This measure is very interesting as it give you an estimate of the "proportion of the data" explained by your model. For example a $r^2$=1 means that 100% of the variance of the data is explained by your model, in other terms your model perfectly fits the data. A $r^2$=0 in the other hand means that your model does not at all explain the data (no fits between your model and the data).

The $r^2$ and the p-value can be computed for any type of fitting, like trying to fit an exponential curve instead of a linear one. What you usually look for when modeling data is the highest $r^2$ possible. As all of this statistics are linked a higher $r^2$ means a lower p-value for an identical number of observations.

• p.values are by themselves not probabilities, and nor do they refer to the probability of observing the fit by random chance only. P.values are the frequencies at which you would expect to see an effect size (be it difference in means, or a goodness of fit) as large as your observed one if the null hypothesis were true. Eg, a null hypothesis for a two sample t.test is that the means of the samples are equal). probabilities are degrees of belief, p.values don't give you the probability of the null hypothesis being true. – Ankur Chakravarthy Apr 6 '15 at 2:06
• @AnkurChakravarthy Frequencies are the exact equivalent of probabilities in this case. Having a frequency of FDR of 0.01 is exactly the same as saying you have 1% chance to observe this fit by random chance (or more precisely to reject the null hypothesis by random chance). I used probabilities as it makes p-values much more understandable (and useful) in my opinion. – cagliari2005 Apr 6 '15 at 2:11