# Calculating software prediction confidance interval

#### Bin

##### New Member
In my job, there is software that calculates a parameter of a product to be manufactured. I have to calculate the software prediction confidance interval.
That target parameter (X), for exemple mecanical resistence, is dependent of variables V1, V2 and V3. The software generates Xs, V1s, V2s and V3s. The software also gives the dimensions (in mm) of the product (P) components (C1, C2, C3). Posterior to the software estimation, 10 products, for example, are to be manufactured with the same especifications (iqual products) using the software given component dimensions. After they are manufactured, for each unit of the 10, X, V1, V2 and V3 are measured, obtaining Xm, V1m, V2m and V3m. There are a manufacturing error (e1) and known measurement error (e2) values.
There is also different types of components (C1a, C1b, C1c). So i also would have to estimate the software prediction confidance for different groups of products , depending on wich components they had, e.g., P1 : (C1a, C2a, C3b), P2 : (C1c, C2a, C3a) ... .
I have data of over a 200 products. For each product:
"P1, C1a, C2a, C3b, Xs, V1s, V2s, V3s, Xm, V1m, V2m, V3m"
My question is: How to best approach this problem? Do i simple estimate the difference in the measured and calculated mean values for each group, considering a t distribution? how to account for the manufactured error? Using regression analysis would be usefull?
Can i even utilize these statistical methods, since it is a non-problability sample?

Any insight wold be of great help.

Thanks!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I think your question gets lost in the way you presented your situation. Go simpler first, you have sample data and you want to calculate prediction intervals? Just for clarification, there is a difference between confidence and prediction intervals and you want the latter, correct?

@Miner - we may eventually need your help here!

#### Bin

##### New Member
@hlsmith, Thanks for responding! Sorry for the confusion. Essentially, i want to know the standard deviation of the software output compared to the measured value. To this, i would have to see how to best group the products by the components (maybe using regression analysis). So each group would have a standard deviation. Then with the standard deviations i would be able to calculate the prediction interval. The problem is that the "true valor " (from measure) also have an error (measuring and manufacturing). And i don't know if i can use a t distribution and simply calculate the difference in the means because it's not a probabilistic sample.