Basic Variables to look at when attempting to discover a new set:
95% range limits: Mean ± 1.95*StdDev.
Confidence interval: The range in which we are x% sure that the population mean (also the regression line) will fall in.
Prediction interval: the range in which we are x% sure that all points will fall in. It is and not influenced by the sample size n.
Statistical Model Analysis: Regression as an example:
Certain questions to answer:
i) Do the residuals appear to be systematically related to the independent variable(s)?
ii) Do the residuals appear to be roughly evenly distributed across the values of the independent variable?
iii) Do the residuals display a fairly constant variability across the values of the independent variable?
iv) Are there any serious deviations from the line expected under normality?