topic Re: Predicted Interval for correlated y vs x in Discussions

Predicted Interval for correlated y vs x

AT — Fri, 09 Jun 2023 00:44:02 GMT

Hi,

I have two variables that are correlated and like to get prediction interval for y vs x at 9.9%. I can do this for linear regression fit. My questions is whether there are other techniques than can accomplish this. I have attached y vs.x with regression line. In particular I like to know what range of x variable gives all the y variable between (a,b) at 99.9% confidence.

Thanks

Adam

Re: Predicted Interval for correlated y vs x

dale_lehman — Fri, 07 Jan 2022 20:23:32 GMT

From the Fit Y by X platform, you can plot (or save) confidence intervals for the fit and/or for individual predictions. Asking for a 99.9% confidence interval is allowed, though that is an unusual choice. For your close association, the 99.9% confidence interval for the fit will probably work, but if you want individual prediction intervals, I believe a 99.9% interval will be too wide to be meaningful.

Re: Predicted Interval for correlated y vs x

AT — Fri, 07 Jan 2022 21:59:58 GMT

Hi Dale,

Thanks so much for quick response. I got the 999% prediction interval shown in attachment. The upper prediction interval is within some of the data. Both x and y are Gaussian. Is it Ok to have data outside upper predication interval ?

Thanks

Adam

Re: Predicted Interval for correlated y vs x

dale_lehman — Sat, 08 Jan 2022 13:19:24 GMT

With this much data you should expect some points to lie outside the confidence interval (regardless of the %). If it is a mean confidence interval, indeed most points would like outside the interval. If they are individual predictions, then fewer should be outside the interval. Since the model is not perfect (it is only a model), of course some points will randomly vary outside the interval.

However, the graph you provide suggests something else is going on. There is an entire section of points outside the interval - this strongly suggests a lurking variable (likely a nominal variable) that is giving two groups of responses. So, conditional on x, y appears to fall into two distinct ranges. Failure to identify this lurking grouping variable means that the resulting confidence interval is too wide - and also, that at least one group will systematically (not randomly) lie outside the interval.

Re: Predicted Interval for correlated y vs x

AT — Tue, 11 Jan 2022 23:23:31 GMT

Thanks Dale. I was able to identify the groups with distinct values and get the prediction interval vs. various groups.

Thanks again.

Regards,

Adam