# what test should be used to tell if two regression lines are significantly different

#### helenekuo

##### New Member
I have two lines in a x-y plot 1. observed migration distance (y) and predicted migration distance (x) (Y=0.95X+0.31, the slope coefficient and the intercept p-value = 0.001)

1:1 line (slope: 1 and intercept: 0)
The null hypothesis is y=ax+b a1=1=a2 and b1=b2

Please kindly advise what test to use to test the hypothesis Thank you

Elaine

#### noetsi

##### No cake for spunky
Re: what test should be used to tell if two regression lines are significantly differ

I am not sure exactly what you are asking. The F test tells you whether the regression line adds signficantly to the model. This in turn is heavily influenced by the difference between the observed and predicted values although I don't think its a statistical test of those two lines in the way you mean.

#### victorxstc

##### Pirate
Re: what test should be used to tell if two regression lines are significantly differ

what test should be used to tell if two regression lines are significantly different
ANCOVA I think.

#### TheEcologist

##### Global Moderator
Re: what test should be used to tell if two regression lines are significantly differ

ANCOVA I think.
I would second that. Also, the standard errors of the slopes are theoretically t-distributed. So in theory you could estimate significance between slopes with a t-test (t-value = (slope1-slope2)/se).

#### noetsi

##### No cake for spunky
Re: what test should be used to tell if two regression lines are significantly differ

I thought ANOVA was looking at whether the separate regression lines for some specific variable (say gender) was signficantly different. Not whether there was a signficant different between the predicted and observed regression line.