Question about linear regression & residuals

#1
I have been reading up on linear regression and residual plots here on stattrek:

http://stattrek.com/regression/residual-analysis.aspx?Tutorial=AP

The page contains the following:

"A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate."

I cant figure out why randomly dispersed points suggest a linear regression model is appropriate; and dispersped points in an ordered manner being inappropriate.

Can anyone elaborate, in layman terms, why this is the case??

Many thanks in advance
 

hlsmith

Omega Contributor
#2
Well how about I flip it back to you and say what if there is a pattern in the error, say they are shaped like a funnel? So they are very small and get larger and larger as the x variable increases.
 

Miner

TS Contributor
#3
Well how about I flip it back to you and say what if there is a pattern in the error, say they are shaped like a funnel? So they are very small and get larger and larger as the x variable increases.
That example might be a little difficult given the way the excerpt was worded.

Try a pattern in the residuals that steadily increased in the first half of the plot then gradually decreased in the second half (e.g., like a frown)?