# Thread: extending"standard error of the estimate" to a confidence interval for all datapoints

1. ## extending"standard error of the estimate" to a confidence interval for all datapoints

I am creating a model that predicts motor input power from various non-electrical measurements. The model includes coefficients that are determined using regression with measured data.

The regression program spits out the "standard error of the estimate". From that I would like to get a confidence interval (at a specified confidence level) of how well the model predicts input power. Can I just multiply the "standard error of the estimate" by the student's t value (which is determined by the confidence level and d.o.f.)? Unfortunately, I've only seen that approach used with the "standard error of the mean" or to find confidence intervals for regression coefficients (e.g. intercept or slope).

Now I have seen in statistics books where they mention doing something similar to find confidence intervals for the y estimate at a specific x value. But I don't want a confidence interval at a specific x value, I want a confidence interval that applies to all the x values. It seems that I should just be able to multiply the "standard error of the estimate" times the student's t value and that's my confidence level for the model with the given data. Does this make sense or am I going crazy?

2. It may not be possible to create fixed confidence interval that applied to all x values. Width of the confidence interval depends on the value of Xis. The CI band will be minimum around the x bar and the band width will increase as x increase/decrease from xbar.

The link below ans example of simple regression, shows how CI band in different xs.
http://www.vias.org/tmdatanaleng/cc_regress_confidiv.html

If the CI band width is not varying much, then you could try average CI width or take the maximum CI band ( Max ( CI at xmin , CI at xmax) ),apply this to all observation.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts