Question

Can someone just point me in the right direction? In which of the following scenarios would it be most acceptable to do an interpolation using a least-squares regression line?

A. There's a high positive correlation.

B. Residuals follow a linear pattern.

C. There's a strong negative correlation, and residuals follow a u-shaped pattern.

D. There's a strong negative correlation, and residuals are randomly scattered around the line y - yhat = 0.

E. There's no correlation, and residuals are randomly scattered around the y - yhat= 0.

Answer 1

1) if residuals show a pattern, then the relationship is not entirely linear.
2) if there's no correlation then there's no point in a linear regression

Answer 2

so not e.
i'm thinking B?

Answer 3

ABCDE - And they're off!

Residuals need to be Random.

ADE - Still in the running

There should be a correlation

AD - Poor old E tripped over a stone on the track.

Residuals should center on y = y-hat

It's D by a nose!

Answer 4

thank you such much for the clear explanation! good rules to go by, thank you1