Question Edited to add more information
I have come across a formula that uses the calculated values from a linear regression,
but I am not sure on how it is useful
lets say for example I have
x = [ 1 2 3 4 5 6 7 8 9 10 11 12]
y = [ 1 2 7 28 6 6 5 27 4 2 6 12]
this gets me an intercept of 7.37 and a coefficient of 0.22
so the linear regression formula is Y = a + b*x
b is the coefficient a is the intercept
Y = 7.37 + 0.22*x
the formula is
if b is greater than 0
number = ((K_max-a)/(b) - last x)
if b is lower than 0
number = ((K_min-a)/(b) - last x)
where
k_max and k_min = are values defined before the calculation for the example
k_max = 25
k_min = 5
last x = is the last value of x, in this case 12
what does this intercept divided in the coefficient means? what does it tells me about my data set?
please let me know if this makes sense, or if this has been used elsewhere
thank you
This is just a guess...
Assuming the linear model is $y=a+bx$, if we let $y=k$ and solve for $x$, we get $\displaystyle x_k=\frac{k-a}{b}$ , in which case, we could interpret $\displaystyle x_k-x_n=\frac{k-a}{b}-x_{n}$ (where $x_n$ is the "last" $x$ value) as the distance along the $x$ axis we must traverse from $x_n$ until the value of the prediction is $k$. This also might be why $k$ is termed a threshold. This might be useful if we want to see how great an extrapolation is required to predict $k$, for example.