In the equation y' = b0 + b1 x1 , y' is level of bordem and x is listening to statistics tutorials. if b1 = 0, what can be said about the relationship between bordem and listening to statistics tutorials?

Assuming that x1 is the x you mention later, the differential equation is

Since , the equation becomes

i.e., the derivative is constant. If the derivative is constant, the original function is a line with slope that constant, i.e. the solution of the differential equation is

So, if , the line grows when x grows, and so the more you listen, the more bored you are.

If otherwise , the line descends when x grows, and so the more you listen, the less bored you are.

Finally, if also , then the derivative is constantly zero, which means that the original function is a constant. So, your level of boredom is always the same, no matter how many hours of tutorials you listen to.

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