I have made several plots using JMP's graph builder with a regression fitted line and the confidence interval gets wider and thinner (see attached below). Doesn't JMP use a confidence interval of 95%? Much appreciation for your helping this novice JMP user and budding statistics learner
Yes, JMP computes and displays 95% confidence intervals of the mean function in the Graph Builder plot you showed.
The confidence interval for the mean response is a 'quadratic form.' It depends on the constant response variance, the design matrix (data), the linear model, and the predictor level.
See this article.
I interpret your surprise at the change in the width of the confidence interval for the mean response to indicate that you have not studied linear regression, so I will not use a mathematical explanation.
Imagine that you have just two observations for X and Y. You fit a line between them. Where is the support for this model? You might think that it is at one or the other observation because that is the physical evidence. It is actually the strongest at the mid-point of the line, even though there are no observations at that point. The reason is that the mid-point of the model is supported equally and maximally by the points to either side. So the confidence interval at the mid-point is shorter than it is at the ends of the line where you observed the response.
Note that the interval length is always strictly in the vertical direction. It is not normal to the fitted line.
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