Regression Analysis - Please explain in laymen terms I'm very new to statistics and I want to be able to interrupt the following regression data. What does y=.33 - .0000007x mean? Also, what is r^2? Please let me know what y, x, and r^2 tells us. 
 
 A: The equation 
$y = 0.33 - 0.000007 * x$ 
where the * = multiplication,  describes the line that you have fitted through your data. A line has two features that define it typically: 1) Where the line intersects with the y-axis (i.e. the value of y when x = 0), and; 2) the slope of the line (I.e. rise over run).
The first number in the equation (0.33) tells you where the line hits the y axis, or the value of y when x is zero. 
The second part of the equation describes the change you observe in y for every unit change you see in x. I.e. y will decrease (because the number is negative) by 0.000007 for every one unit change you see in x. This equation effectively lets you plug in a value of x and then work out what you would expect the y value would be.
$R^2$ however tells you about the strength of the relationship between the two variables. $R^2$ values can take any value between 0 and 1. A value of 1 means the two are perfectly correlated. A value of 0 means that there is no statistically significant relationship between the two variables. It can also be interpreted as the predictive capacity of your model to a degree. A high $R^2$ suggests that the two variables could be used to predict one another - for instance a $|R^2|$ of 0.9 means that your model captures 90% of the variation in your data. 
However, Your value is very close to zero and suggests that the model only describes 0.07% of the variation in your data. It probably does not help that you have chosen to fit the wrong kind of regression line to your data though (I think). I suspect you have fitted what is called a simple linear regression between these two variables, which assumes a certain kind of response - one that can theoretically range between negative infinity and infinity. Your response, since it is a percentage, can only range between 0 and 100, meaning that you really need a different kind of model - probably a binomial regression. Here is a link that goes into this further if you want to find out more.
