How can I develop a 5-variable equation for five linear relationships?

[350Z]

How can I develop a 5-variable equation from five linear relationships?

I have 5 variables that impact a result, let's call it "TC". When I evaluate each variable independently (with the rest of the variables constant), per plotting these I know they are linear and follow these y=mx+b equations.


y1 = -0.9890 * X1 + 8.655, y2 = 0.2340 * X2 + 8.670, y3 = 5.0633 * X3 + 5.037, y4 = -3.3136 * X4 + 12.674, and, y5 = -3.0745 * X5 + 11.285


when, (x1 x2 x3 x4 x5) = (x1, 0, 5, 6.5, 6.5), (0, x2, 5, 6.5, 6.5) (0, 0, x3, 6.5, 6.5), (0, 0, 5, x4, 6.5), and, (0, 0, 5, 6.5, x5) for each of the equations respectively.


I also know that x1 is between -5 and 5, x2 is between -5 and 5, and, x3 is between 1 and 7.


So, how can I develop a 5-variable equation to be able to change any of these and get a new TC (or y) value as the output? Thank you!
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[Deleted member 4993]

I have 5 variables that impact a result, let's call it "TC". When I evaluate each variable independently (with the rest of the variables constant), per plotting these I know they are linear and follow these y=mx+b equations.


y1 = -0.9890 * X1 + 8.655, y2 = 0.2340 * X2 + 8.670, y3 = 5.0633 * X3 + 5.037, y4 = -3.3136 * X4 + 12.674, and, y5 = -3.0745 * X5 + 11.285


when, (x1 x2 x3 x4 x5) = (x1, 0, 5, 6.5, 6.5), (0, x2, 5, 6.5, 6.5) (0, 0, x3, 6.5, 6.5), (0, 0, 5, x4, 6.5), and, (0, 0, 5, 6.5, x5) for each of the equations respectively.


I also know that x1 is between -5 and 5, x2 is between -5 and 5, and, x3 is between 1 and 7.


So, how can I develop a 5-variable equation to be able to change any of these and get a new TC (or y) value as the output? Thank you!
.

Have you tried ANOVA ?

 

[350Z]

Have you tried ANOVA ?

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Thank you very much for the quick response, it's certainly appreciated!

Anyway, I did not know about ANOVA, so, I just performed a search and will read up a little bit to see how it can help me in resolving my question. Again, thank you!

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[350Z]

Have you tried ANOVA ?

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Thank you very much for your response so quickly, much appreciated!

No, I have not tried ANOVA, thus, researching to see if it can help me out right now. Thanks for the tip. Also testing if the embedded MS Excel Solver can help me with the analysis. I did try the Simplex LP Solver (along with 2 more), yet, when I performed the post tests it was not yielding the proper results.

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[350Z]

So each "given" amount could be stored and above could be:

y1 = -0.9890 * X1 + 8.655 : y1 = u1 * x1 + v1

y2 = 0.2340 * X2 + 8.670 : y2 = u2 * x2 + v2

y3 = 5.0633 * X3 + 5.037 : y3= u3 * x3 + v3

y4 = -3.3136 * X4 + 12.674 : y4 = u4 * x4 + v4

y5 = -3.0745 * X5 + 11.285 : y5 = u5 * x5 + v5

Yes?

Curious: I used lower case x's; any reason you use the BIG X ?

Your new variable equations (using u1...u5) are correct! I usually do use lower case "x" as well. Thus, no reason behind the CAP X's. One thing to re-iterate is that I actually want to get to a y(as a function of x1,x2,x3,x4,x5) =..... type of equation. My overall "y" is dependent on all 5 variables. In order to analyze each of the 5 variables independently to see if they were linear, I started by keeping the other 4 at a constant value. Thus, arriving at the y=mx+b solutions.

Thank you!
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[350Z]

I ran a quick ANOVA test on excel, yet, not sure how I will be able to develop an equation with the results. Nor, can I interpret them in a way that could help me arrive at such.

Any insights on the results would be helpful. Thank you!

Anova: Two-Factor With Replication
SUMMARY	FC	FT	C	FRH	RRH	Total
LC
Count	5	5	5	5	5	25
Sum	43.28	43.33	41.11	45.5	46.79	220.01
Average	8.656	8.666	8.222	9.1	9.358	8.8004
Variance	16.62213	0.93298	3.03632	0.29215	0.12577	3.66283733
RC
Count	5	5	5	5	5	25
Sum	-6.23	-6.1	-4.61	-7.82	-7.19	-31.95
Average	-1.246	-1.22	-0.922	-1.564	-1.438	-1.278
Variance	16.70133	0.0209	1.70427	0.02918	0.06822	3.13700833
Total
Count	10	10	10	10	10
Sum	37.05	37.23	36.5	37.68	39.6
Average	3.705	3.723	3.65	3.768	3.96
Variance	42.04642778	27.5720011	25.3326889	31.73195111	32.46222222
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	1269.676832	1	1269.67683	321.1668234	1.02199E-20	4.08474573
Columns	0.565508	4	0.141377	0.035761542	0.997450952	2.60597495
Interaction	4.497788	4	1.124447	0.284430701	0.88634404	2.60597495
Within	158.133	40	3.953325
Total	1432.873128	49