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A confidence interval is an interval that covers an unknown parameter with $100(1-\alpha)\%$ confidence. Confidence intervals are a frequentist concept. They are often confused with credible intervals which is the Bayesian analog.
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Residuals and Confidence Intervals in a Simple Linear Regression
Regarding your comment " I'm simply not used to the visual aspects of graphing smaller data sets." here is your data with 3, 4, 5, and finally all 6 data points. Notice the progressively tighter confi …
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Confidence limits on a curve fit with algebraically related parameters
As an alternative answer, I found that a quadratic logarithmic equation "y = a + b * log(x) + c * pow(log(x), 2.0)" (where log is the natural log) seems to fit the entire range of the posted data fair …