Analogies Between
Mean + Standard Deviation
and
Simple Regression

 

Mean + Std. Dev.

Regression

This description is intended for --
data whose histogram is single humped, not badly skewed, and not rife with outliers.
This description is intended for --
data which lies in a band about a straight line which is of roughly constant width, not rife with outliers.
Look at a Histogram (or stem+leaf plot) before using this method. Look at a Scatter Plot   before using this method.
Beware of Outliers Beware of Outliers
Mean
Specified by ONE number
Least squares line
Specified by TWO numbers
Residual
Distance from the mean
Residual
(Vertical) distance from the line
s, the Standard Deviation  
 
 

"Typical" residual
s or sy|x or others ...  
Alas, both name and notation of this entity differ amongst books & statistical packages.
"Typical" rsidual
2/3 Rule (approximate)
Often about 2/3 of the data is within ±2s of the sample mean
2/3 Rule (approximate)
Often about 2/3 of the data is within a ±2s (vertical) distance of the line.
Confidence Interval for Population Mean
Bounded by a pair of points within which we are __% sure the population mean lies. For large samples the 95% interval is approximately ±2s about the sample mean

(Calculation: Easy, use the square root rule and the t-distribution)

Confidence Band for Population Line
Bounded by a pair of curves within which we are __% sure the population line lies. For large samples the 95% band is about ±2s above and below the sample regression line.

(Calculation: Harder, but many statistical packages will plot the curves for you.)