Non-linear Regression Interactions

Question 1

What are the three steps of using regression to test for non-linearity?

Answer 1

1. Mean-centre the continuous IV
2. Calculate the cross-product (HERE it is SQUARING the mean-centred variable)
3. Regress the DV on the IV using sequential regression - enter the mean-centred IV, then enter the cross-product/quadratic term

Question 2

How do you know if the function is not linear?

Answer 2

If p<.05 for the cross-product based on the test for change in R^2 or b, results indicate a significant non-linear relation/effect of the IV on the DV

If p>.05 for the cross-product based on the test for change in R^2 or b, results indicate the relation/effect of the IV on the DV does not significantly deviate from linearity

Question 3

What do the values of b1 and b2 indicate when testing for linearity using regression?

Answer 3

b1 - magnitude of the linear trend

b2 - magnitude of the rate of change (if linear=0) - you can also use this value to tell the sign of the quadratic (+=turned up, -=turned down)