Solved – Residuals and Confidence Intervals in a Simple Linear Regression

So this question is a little different from any of the other questions asked about this topic. I have a simple linear regression in R and it lists the residuals and has 'relatively large' confidence intervals relative to the set of data. I would really like to show the statistical significance of this model and would like a little more than just a nice $p$-value and high $R^2$ value to show, and the confidence intervals diminish this.

  • 6 data points, actual graph w/h confidence intervals shaded grey:

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  • Output from the call to lm:

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Would it help to graph the residuals along the normal?

In addition, how useful would it be to share the F statistic or the standard error with the residuals or the intercept to support the statistical validity of my regression despite the sub-optimal confidence intervals?

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 confidence intervals. All graphs have the same scales. This is effectively a visual illustration of Peter Flom's advice in the comments.

Three Data Points:


Four Data Points:


Five Data Points:


Six Data Points:


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