I am working on a business case problem for my company (CPG) and was asked to come up with a way to predict Customer Order Fill Rate (CFR) based on the amount of inventory we hold.
Now I have come up with a formula to estimate CFR based on the cases of inventory we hold using regression, however I was asked about the probability that my estimated CFR will be correct.
So if my regression formula suggests in the future that having 100 cases of product XYZ will result in an estimated CFR of 98%, the business team asked me what is probability of actually achieving that CFR.
But I was wondering if there is a way to give such a probability on a single point estimate? I mean I am aware that I could use a prediction interval (I guess is more accurate for this case than confidence interval) to say the I am 95% confident that the future point estimate will be within a range. But I wanted to confirm if there is any such thing (a confidence %) for a single point estimate.
So my observed data set for building the regression is something like this:
My inventory data set is from 0-100 cases (not unique values, I can have duplicate inventory values with different CFR).
For regression I plot from 0-100 cases (taking the average CFR for each point) and build a curve for it. Here's is the regression formula I determined:
With this formula, the input is the inventory (number of cases) and the output is the projected CFR.
I want to know how I can determine (or if its even possible) to get a probability value of in the future actually achieving the CFR (point estimate).
My regression formula has an x (inventory (cases)) and y (CFR): the formula determines if x = 15 then y = 93.4%.
But what is the probability that my estimation of 93.4% CFR from x = 15 will be correct? Is there a way to give confidence % for the point estimate of 93.4% CFR?