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In: Statistics and Probability

Three variables are used to monitor a chemical process. They are X1 percentage impurities, X2 temperature...

Three variables are used to monitor a chemical process. They are X1 percentage impurities, X2 temperature F, and X3 concentration. The initial sample of 14 observations is listed in the following table. (a) Plot the data on a matrix scatter plot and comment on any observed collinearity. (b) Perform principal components analysis in Minitab using the correlation matrix option. Identify the principal components that explain the majority of the variation. Use the first two principal components. Compute the principal components scores of the first two principal components and construct a matrix scatter plot of the z-

Sample X1 X2 X3
1 16.92 84.50 43.26
2 16.80 58.21 43.44
3 17.38 84.23 42.74
4 16.80 85.74 43.60
5 16.82 85.53 43.18
6 16.71 85.49 43.72
7 17.07 84.29 42.83
8 16.83 85.32 43.41
9 16.71 85.78 44.28
10 16.88 84.87 43.09
11 16.73 85.68 44.00
12 16.87 85.03 43.78
13 17.60 84.10 42.11
14 16.80 85.38 43.48

scores to determine if the selected principal components appear to be randomly distributed? (c) Create standardized z-scores principal components individuals control chart.

Solutions

Expert Solution

Three variables are used to monitor a chemical process. The Variables are X1 percentage impurities, X2 temperature F, and X3 concentration.

(a) Plot the data on a matrix scatter plot:

## The variables X1 and X3 are negatively correlated.

(b) Principal components analysis in Minitab using the correlation matrix option:

Principal Component Analysis: X1, X2, X3

Eigenanalysis of the Correlation Matrix

Eigenvalue 1.8814 1.0034 0.1152
Proportion 0.627 0.334 0.038
Cumulative 0.627 0.962 1.000


Variable PC1 PC2 PC3
X1 0.708 -0.026 0.706
X2 0.034 -0.997 -0.071
X3 -0.706 -0.074 0.704

## First two principal components explain the majority of the variation.


Scree Plot of X1, ..., X3:


Score Plot of X1, ..., X3

Matrix scatter plot of the z-scores:

  ## The selected principal components appear to be randomly distributed.

(c) Standardized z-scores principal components individuals control chart:

orchestra answered 2 years ago
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