How to interpret the slope in this chart?

Question

I have a chart that was generated from a linear regression. It looks like this:

I see that it's slope is slightly down. The slope I get from the linear regression, however is -1.3081201334816588E-9

I am not sure how to interpret this. I want to know many many degress it is inclined upwards or downwards. So for this line I'd want to see something like -3 or -5 degrees

How can I interpret and convert that slope given by the calculation I have to the number of degrees up or down from zero (completely horizontal)?

Answer 1

The slope of that line is $$ -1.3 \times 10^{-9} $$ measured in (units of $y$ / units of $X$).

That is a very very small number. For very very small numbers, $\tan \theta \approx \theta$, so that is also the slope of the line when measured in radians.

That's about $-7.5 \times 10^{-8}$ degrees.

On your picture it looks like $-3$ or $-5$ degrees because the units on the $y$ axis are much much smaller than the units on the $X$ axis.

Answer 2

The slope is more or less $\frac{y}{x}$ (at the limit), which indeed is the tangent of the triangle builded from the inclined line, a vertical and a horizantal. Then just take $\arctan$.