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This topic contains 6 replies, has 4 voices, and was last updated by Chris Seider 1 week ago.
I am confused on a simple basic question, how to explain main effects when the interaction is significant… let’s take this model here as an example…y = x1 + x2 -x3 – x1:X3 + x1:x2
” : ” stands for interaction….
How would you explain the effect of x1? Here the manufacturing engineer want to know how much is the effect of each individual variable and what direction does he has to move the variables x1, x2, and x3 to make the process better…
The easiest way to do it is graphically. Put together a 3D plot with x1 along one axis and x2 along the other. Freeze x3 at its midpoint and generate the surface based on x1 and x2. Rotate the plot so you can see both X1 and X2 axis. The effect of X1 acting alone will correspond to the line on the plane of X1, Y where X2 = its minimum and conversely. The rest of the surface will illustrate what happens when both are changing.
If you don’t have 3D plotting capability then plot the lines for the function Y = X1 where you have frozen X3 at its midpoint and X2 is set first at its minimum and then its maximum value. The two lines will not be parallel and the area between them will define, in 2D space, the region over which Y will vary as both X1 and X2 change.
Thank you Robert for the response… I will use the 3D plot to explain interaction. Can i use the coefficient of individual factors and use that also to explain the effects. In the previous example let’s say the coefficients are this 290 = 65 + 6×1 + 7×2 -9×3 – 2×1:X3 + 3×1:x2
In this case is it correct to say the effect of x1 is “approximately” 6-2+3 (these are coefficients of x1, x1:x3, and x1:x2)..After i wrote this sentence i can feel it this is not correct…. If this is not correct, then what will be the coefficient of x1 and its direction from the above equation so that the manufacturing person can dial the knob?
Robert: Can you please answer the question above when you get a chance?
The only way you could make that statement would be if you have a situation where both X2 and X3 have values of 1 and you would have to mention the fact that the estimate for the effect of X1 is for that specific combination of X2 and X3.
If X2 and X3 do not have values of 1 then the better bet would be to generate that expression for X1 at the midpoints of X2 and X3 and, as before, note that this is what you have done.
The issue is that when interactions matter you can no longer make simple statements concerning the impact of a single variable since the final effect of that variable can only be expressed in terms of the other variables in the interaction.
Thank you so much Robert for the help. Wish i can be as good as you in this stuff!!!!!!!!!!
If you have the coded equations, you can substitute values from -1 to +1 for each variable but Minitab has tools and equations for uncoded equations–just gets a tad tricky with center points if they were in your model. The centerpoints term is meant to apply a +1 if you’re at the center point or 0 if not since the curvature can’t be described with basic factorial designs.
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