Determine resulting least-squares equation of Multiple regression using matrix approach.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter11: Nonlinear Programming
Section11.2: Introductory Concepts
Problem 11P
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By studying a chemical process,
expects the yield to be affected
by the levels of two factors, X1
and x2.
Observation
Factor 1
Factor 2
Yield
(X)
(x2)
29.1
(v,)
251.3
Number
1
41.9
2
43.4
29.3
251.3
3
43.9
29.5
248.3
Observations
recorded
for
4
44.5
29.7
267.5
5
47.3
29.9
273.0
various levels of the two factors
47.5
30.3
276.5
are shown in the following table.
• Interaction between x, and x2 is
expected
knowledge of similar processes.
7
47.9
30.5
270.3
50.2
30.7
274.9
9
52.8
30.8
285.0
10
53.2
30.9
290.0
not
based
on
11
56.7
31.5
297.0
12
57.0
31.7
302.5
13
63.5
31.9
304.5
Units of the factor levels and the
14
65.3
32.0
309.3
15
71.1
32.1
321.7
yield
analysis.
Determine resulting least-squares
equation of Multiple regression
using matrix approach.
ignored for the
are
16
32.5
32.9
77.0
330.7
17
77.8
349.0
34
Transcribed Image Text:By studying a chemical process, expects the yield to be affected by the levels of two factors, X1 and x2. Observation Factor 1 Factor 2 Yield (X) (x2) 29.1 (v,) 251.3 Number 1 41.9 2 43.4 29.3 251.3 3 43.9 29.5 248.3 Observations recorded for 4 44.5 29.7 267.5 5 47.3 29.9 273.0 various levels of the two factors 47.5 30.3 276.5 are shown in the following table. • Interaction between x, and x2 is expected knowledge of similar processes. 7 47.9 30.5 270.3 50.2 30.7 274.9 9 52.8 30.8 285.0 10 53.2 30.9 290.0 not based on 11 56.7 31.5 297.0 12 57.0 31.7 302.5 13 63.5 31.9 304.5 Units of the factor levels and the 14 65.3 32.0 309.3 15 71.1 32.1 321.7 yield analysis. Determine resulting least-squares equation of Multiple regression using matrix approach. ignored for the are 16 32.5 32.9 77.0 330.7 17 77.8 349.0 34
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