Question

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?

Answer 1

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

`y' = b_0+b_1x`

Since
`b_1=0`, the equation becomes

`y' = b_0`

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

`y = b_0x+c`

So, if
`b_0>0`, the line grows when x grows, and so the more you listen, the more bored you are.

If otherwise
`b_0<0`, the line descends when x grows, and so the more you listen, the less bored you are.

Finally, if also
`b_0=0`, 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.