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Community Trekker

Joined:

Jun 23, 2011

## How to compare two regression coefficients?

Hi, i have a data set with:
2 groups: A and B
for each case, 2 variables: var1 and var2
i'd like to compare regression coefficient R2 and R2 (between the 2 groups) for the regression curves: var1=R1*var2 and var2=R2*var2

I know how to obtain R1 and R2 (fit y by x (var2=y and var1=x), group by "group", but I don't know how to compare R& and R2 to say there are not equal (or R1>R2).

Nicolas
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Super User

Joined:

Jun 23, 2011

Solution

## Re: How to compare two regression coefficients?

Here is what I would try:

Arrange your data table vertically with three columns: Group (nominal), X and Y (both numeric).

The you can use the Fit Model platform. add Y to Y, and to the effects add Group, X and group*X

The latter is the interaction variable related to any difference in slope. This is obtained by selecting the Group and X in the left list and click on "cross". Alternatively, select Group and X and choose "Full Factorial" from the Macros drop down list. Remember to select the "No intercept" check-box. Personality should be standard least squares (usually default). Run Model!

In the report look at the p-value (Prob > F) for Group*X. The smaller value, the more likely it is that the regression slope coefficients are different.

I use to call method is called Analysis of Covariance (ANCOVA). But I am not sure that it strictly an ANCOVA when there are no intercept parameter. There of course some assumptions about normality etc the need to be met to justify this type of analysis.
4 REPLIES 4

## Re: How to compare two regression coefficients?

Perhaps you could clarify, perhaps you have a typo.

"var1=R1*var2 and var2=R2*var2" — should that second part be var1=R2*var2 ?

Further, you state var2=y and var1=x, and this doesn't seem to fit either. Seems backwards to me.

Lastly, regression equations usually use b1 and b2 as the regression coefficients, the equation is usually written as y=b0+b1X, and R2 usually denotes the r-squared value. Are you implying that your model contains no intercept?

I would need to know these things before I feel comfortable providing an answer.

Community Trekker

Joined:

Jun 23, 2011

## Re: How to compare two regression coefficients?

Hi, thank's, you're right I'm not cool with stat stuffs...

OK, I meen:

two variables: x and y
two independent groups: 1 and 2

I have two regression lines : y=0+b1x for 1st group and y=0+b2x for the second group.
The two lines cross "0,0"
I want to show that b1 is different from b2

Super User

Joined:

Jun 23, 2011

Solution

## Re: How to compare two regression coefficients?

Here is what I would try:

Arrange your data table vertically with three columns: Group (nominal), X and Y (both numeric).

The you can use the Fit Model platform. add Y to Y, and to the effects add Group, X and group*X

The latter is the interaction variable related to any difference in slope. This is obtained by selecting the Group and X in the left list and click on "cross". Alternatively, select Group and X and choose "Full Factorial" from the Macros drop down list. Remember to select the "No intercept" check-box. Personality should be standard least squares (usually default). Run Model!

In the report look at the p-value (Prob > F) for Group*X. The smaller value, the more likely it is that the regression slope coefficients are different.

I use to call method is called Analysis of Covariance (ANCOVA). But I am not sure that it strictly an ANCOVA when there are no intercept parameter. There of course some assumptions about normality etc the need to be met to justify this type of analysis.

Community Trekker

Joined:

Jun 23, 2011

## Re: How to compare two regression coefficients?

Hi, thank's.

it works

And for Prob > F, can I take 0,05 as a significant value?