Re: plotting regression lines after an ANCOVA

What you have, of course, is an ordinary least squares regression with
a response related to two variables. The fact that one variable is a
"covariate" is of no great importance.
That fact that this is called ANCOVA is not a big deal. It's just least
squares.

I don't understand this: "I have specified a linear model (in R): y ~
x1 * x2."
My first reaction to it was "X1 multiplied by X2, hence the X1, X2
interaction."
I suspect you meant Y = bo + b1*X1 + b2*X2 + b12*X1*X2"

Given that b12 is not significant, then, as you said there is no X1,X2
interaction.
In which case the reduced model is just Y = bo + b1*X1 + b2*X2

Assuming both b1 and b2 are significant, then the best way to present
this would
be two parallel lines. That is, Y vs X1 with X2 as a parameter.

If b2 is not significant then you just have one line... Y vs X1. OMU




Henrik wrote:
Dear all,

I would appreciate some advice on a discussion I had with a collegue
regarding plotting regression lines after having done an ANCOVA.

I have a continuous response variable y, which depend on a factor x1
(with four levels) and a continuous covariate x2. I have specified a
linear model (in R): y ~ x1 * x2. In the ANOVA-table, the interaction
x1:x2 is not significant, i.e. the slope of y on x2 does not differ
significantly between levels of x1. However, there is a significant
effect of x1 on y.

What would be the most appropriate way to present the result
graphically? Should I plot separate regression lines with different
slopes (despite the fact that they are not significantly different) and
then write in the figure text that the regression lines are there
'just' to show the patterns? Or should I simplify the model to 'y ~ x1
+ x2' and plot a common slope for all years? Is just a matter of taste?
I am curious about your opinion!

Thanks for taking your time!

Best regards,

Henrik

.

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