Scenario 5-Dummy Variable

It seems that I am understanding the dummy variable section's various tricks and traps (using not just D but D* (x-9) etc).  However, while my other numbers seem on par, I actually have something like a ESS=32 for scenario 1 and 27 for scenario 5 with the dummy variable (flipped from the sample illustrative sheet), therefore, while my TSS has increased, my ESS has decreased (NOT moving in tandem with TSS)!!!

Can someone please help me?  I've checked and rechecked and everything seems good except this.  I think I'm all done with this project except for this project, and so far I've thought I understood it clearly!

Many thanks in advance NEAS for an expedient answer.

	Part 5 (Dummy Variable)	Part 4 (No Dummy Variable)	Part 1 (Stable Rates)
Estimate of sigma	0. 484399	0.820495	0.522311
Estimate of beta2	-----------	0.160615	0.13747
Standard error of beta2	-----------	0.023795	0.015141
adjusted R2	0.828522	0.49529	0.69494
TSS	158.7295	158.7295	106.4193
ESS	27.21854	78.76587	31.91866

[NEAS: Your results are expected.  The sigma is greater (by random fluctuation) in the stable rates simulation (52.2% vs 48.4%), so the ESS is also higher (31.9 vs 27.2).  If you run a second simulation, you might get the opposite results.]

The key is that you are not transforming the equation to adequately represent your data.  The piecewise linear regression section in the book (p.136) may be helpful.

also see at this link.  It is quite clear.

http://www.neas-seminars.com/discussions/download.aspx?id=1198&MessageID=5383

I'm not quite sure I follow.  I thought this is what I've been doing, following the format from your link. What am I missing? What do you mean by transforming the data?  What did I miss to do??

I am guessing that you got to the "V" or inverted "V" shape on the residual plot but are having difficulty correcting for it so that your error plot looks random again. 

I also ran into that.  In that case, the actual graph (not the residual graph) is a linear function up to your critical point, then another linear function.  Your regression equation needs to reflect that change, and have enough variables to match your data.

On the second page of the sample project I linked, the author adds a dummy variable and says:

The regression equation becomes:

            

Y = a₁ + B₁X1 + B₂X₂ + Da₂ + DB₃X₂  - DB₂X₂

 where a2 is his critical point.  He (and you) need to transform his(your) equations into new variables which are the linear combinations of D and X2.  The author says:

x₁ = X1,            x₂ = X₂ – D(X₂ – 9),                x₃ = D(X2-9)

 

and then creates a plot where these new variables are the independent variables.  (Note that 9 is his critical point).  The error should then look random again.

 

Hope this helps