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I'm a novice trying to learn about statistics in the infrastructure asset management industry.

I have an existing exponential regression equation that is used to find the condition of a given asset:

$${Y} = A + Be^{CX}$$

I'm trying to determine what each of the variables in that equation represent. Here is what I think I know:

  • ${Y}$ is the asset condition.
  • ${B}$ is $-1$, so it can be ignored.
    • I believe we use $-1$ so that the line will point downwards. Otherwise, exponential regression lines normally point upwards.
  • $e$ is the inverse of the natural logarithm of a number.
  • ${C}$ is an exponential regression coefficient.
  • ${X}$ is the age of the asset in years.

Question:

I'm not sure about $A$. For my purposes, I believe the value would always be $21$, which is the maximum condition an asset can ever be ($20$), plus $1$.

But what does $A$ represent? Is it the $y$-intercept?

  • If so, I find that confusing, because the asset condition can't ever be $21$. The maximum condition is $20$. So, I don't understand how the y-intercept could be $21$.
User1974
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    Conceptually $A$ is $\lim_{X \to -\infty} Y$ if $C>0$ or $\lim_{X \to +\infty} Y$ if $C<0$. In other words it is the $y$ value of the horizontal asymptote. This might not matter in your application if your time interval if, say, $C>0$ and $X \geq 0$, though. In this scenario the best way you can think of $A$ is really just $Y(0)-B$ (not super intuitive I admit). – Ian Jan 02 '22 at 02:38
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    @Ian : Thanks, I think you were right about thinking of $A$ as being $Y(0) - B$. I ended up at that same conclusion on my own too. I posted by thoughts as an answer. Cheers! – User1974 Jan 02 '22 at 14:08

1 Answers1

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My best guess:

$Be^{CX}$ is always going to be at least $1$ or greater. Even when the age is $0$, $Be^{CX}$ will still be $1$. The reason being, $e^0$ is equal to $1$, because any number to the power of zero equals $1$.

So, in order for the asset condition to be $20$ when the age is $0$ (when the asset is new/in perfect condition), we need to set $A$ to $21$ so that when we subtract $1$, $A$ will be $20$ (as expected).

Therefore, $A$ is the y-intercept, which is effectively $21 - 1$ (aka $Y(0) - B$).

User1974
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