# Thread: Comparing coefficients from two separate regressions

1. ## Re: Comparing coefficients from two separate regressions

Of course multicolinearity influences the evaluations of individual parameter estimates. But how does it influence a Chow test?

(By the way: MC is often an abbreviation for Markov Chain or Monte Carlo.)

2. ## Re: Comparing coefficients from two separate regressions

I doesn't as far as I know. I never commented on MC in regards to a chow test.

Pretty much everyone in analsys uses their own nomeclature. For instance SEM stand to some for structural equation models and to others standard error of the measurment. I doubt the OP thought I was talking about either monte carlo simulations or markov chains - which never came into this discussion.

3. ## Re: Comparing coefficients from two separate regressions

Did Shakespeare write a play about 'much ado about nothing'?

I wish the original poster good luck – if it happens that she returns to this thread.

4. ## Re: Comparing coefficients from two separate regressions

Reviving this thread...

I'm evaluating two (2) refrigerants (gases) that were used in the same refrigeration system.

I have saturated suction temperature (S), condensing temperature (D), and amperage (Y) data for the evaluation.
There are two (2) sets of data; 1st refrigerant (R1) & 2nd refrigerant (R2).

I'm using a non-linear, multivariate (S & D), model for the regression analyses;
polynomial of the 3rd degree.

I would like determine how much less/more amperage on average, as a percentage, is being drawn by the second refrigerant.
Or, some similar metric as a performance comparison.

First thought was :
1. Determine the model to use...
Y = b0 + b1*S + b2*D + b3*S*D + b4*S^2 + b5*D^2 + b6*S^2*D + b7*D^2*S + b8*D^3 + b9*S^3
2. Derive coefficients (b) from the baseline data (R1).
3. Using those coefficients, for each S & D in the R2 data set, calculate each expected amp draw (Y-hat) and then average.
4. Compare that Y-hat average to the actual average amp draw (Y2) of the R2 data.
5. percent (%) change = (Y2 - Y-hat) / Y-hat

However, since the 2nd refrigerant has slightly different thermal properties & small changes were made to the refrigeration system (TXV & superheat adjustments) I don't believe this 'baseline comparison method' is accurate.

Next thought was to do two (2) separate regression analyses:
Y1 = a0 + a1*S1 + a2*D1 + a3*S1*D1 + a4*S1^2 + a5*D1^2 + a6*S1^2*D1 + a7*D1^2*S1 + a8*D1^3 + a9*S1^3
&
Y2 = b0 + b1*S2 + b2*D2 + b3*S2*D2 + b4*S2^2 + b5*D2^2 + b6*S2^2*D2 + b7*D2^2*S2 + b8*D2^3 + b9*S2^3

and then, for saturated suction temp (S), compare coefficients (a1 vs b1)...
% change = (b1 - a1) / a1

However, again, these coefficients should be weighted differently...
Therefore, the results would be skewed.

I believe I could use a Z-test to determine how differently weighted the coefficients are, but I'm not sure I fully understand the process, or meaning of the output.
Z = (a1 - b1) / sqrt ( SE[a1]^2 + SE[b1]^2 )
But, that still wouldn't give me a performance metric, which is the overall objective...
And, I believe the Z-test can't be used on non-linear regression models either, correct?

There's also the option of adding a dummy variable (interacting variable), but I'm not so familiar with how to interpret a performance metric from the regression results...

Help?!

Thanks in advance,

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