The idea is: We have data (here it are the tuples: (monarch egg production,overwintering population)). We ask ourselves if there may exist a lineair relationship between the two.
This question may look odd to you. Why would we care of a linear relationship?
Well, it is important to get more insight in the thing you want to study.
See this example:
We measure the force $F$ needed on a spring to get a displacement $x$ from the initicial length of the spring. Physics tells us there is a lineair relationship between them: $F = kx$. Notice $m=k$ and $b=0$ in this case.
If we can find 'the best' fitting line between the data, we can then find the 'best' value of $k$ to explain our data. But this value represents properties of the material from wich the spring is made and this can be verry important to know.
But there doesn't always exists a linear relationship in the data. It may be unclear wether there is such a relationship or not. We need a sort of test wich says yes or no. The values $F_{1,11}, r^2$ and $P$ are the outcomes of such tests. The most intuitive value and probably most important to you is: $r^2$. $r^2$ is the percentage of the data wich can be explained with the linear model. In this case it is $0.47$ and isn't verry much. From the graph you can see that indeed the data isn't well fitted.
You cannot know the values $m$ and $b$ from $F_{1,11}, r^2$ and $P$. These values only tells us information about the statistics of the fit.
There is one exception and it is when $P$ is close to $1$. In this case the 'best fitting' line is the horizontal line.
