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a. Compute the first principal component score for observation 1. (Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign.) PC1,1 b. Compute the second principal component score for observation 2. (Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign.) PC22 c. Compute the third principal component score for observation 3. (Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign.) PC33

a. Compute the first principal component score for observation 1. (Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign.) PC1,1 b. Compute the second principal component score for observation 2. (Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign.) PC22 c. Compute the third principal component score for observation 3. (Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign.) PC33

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Principal Component Analysis Exercise** 1. **Compute the First Principal Component Score for Observation 1** - *Instruction*: Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign. - Formula Box: \(PC_{1,1}\) [Input box] 2. **Compute the Second Principal Component Score for Observation 2** - *Instruction*: Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign. - Formula Box: \(PC_{2,2}\) [Input box] 3. **Compute the Third Principal Component Score for Observation 3** - *Instruction*: Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign. - Formula Box: [Input box]
Transcribed Image Text:**Principal Component Analysis Exercise** 1. **Compute the First Principal Component Score for Observation 1** - *Instruction*: Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign. - Formula Box: \(PC_{1,1}\) [Input box] 2. **Compute the Second Principal Component Score for Observation 2** - *Instruction*: Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign. - Formula Box: \(PC_{2,2}\) [Input box] 3. **Compute the Third Principal Component Score for Observation 3** - *Instruction*: Round intermediate calculations to at least 4 decimal places and your final answer to 4 decimal places. Negative value should be indicated by a minus sign. - Formula Box: [Input box]
The following table displays the weights for computing the principal components and the standardized data (z-scores) for three observations. | Weight | \(PC_1\) | \(PC_2\) | \(PC_3\) | |--------|--------|--------|--------| | \(x_1\) | -0.65 | 0.69 | 0.60 | | \(x_2\) | -0.70 | 0.12 | -0.84 | | \(x_3\) | 0.72 | 0.86 | -0.33 | --- | | \(Z_1\) | \(Z_2\) | \(Z_3\) | |--------|--------|--------|--------| | Observation 1 | 0.82 | 0.40 | -0.31 | | Observation 2 | 2.81 | 2.61 | -1.22 | | Observation 3 | -0.89 | -1.12 | 1.39 | The first table contains the weights assigned to each variable (\(x_1, x_2, x_3\)) for the computation of the principal components (\(PC_1, PC_2, PC_3\)). The second table shows the standardized data or z-scores (\(Z_1, Z_2, Z_3\)) for three observations. Each cell represents the z-score of a particular observation for the corresponding principal component.
Transcribed Image Text:The following table displays the weights for computing the principal components and the standardized data (z-scores) for three observations. | Weight | \(PC_1\) | \(PC_2\) | \(PC_3\) | |--------|--------|--------|--------| | \(x_1\) | -0.65 | 0.69 | 0.60 | | \(x_2\) | -0.70 | 0.12 | -0.84 | | \(x_3\) | 0.72 | 0.86 | -0.33 | --- | | \(Z_1\) | \(Z_2\) | \(Z_3\) | |--------|--------|--------|--------| | Observation 1 | 0.82 | 0.40 | -0.31 | | Observation 2 | 2.81 | 2.61 | -1.22 | | Observation 3 | -0.89 | -1.12 | 1.39 | The first table contains the weights assigned to each variable (\(x_1, x_2, x_3\)) for the computation of the principal components (\(PC_1, PC_2, PC_3\)). The second table shows the standardized data or z-scores (\(Z_1, Z_2, Z_3\)) for three observations. Each cell represents the z-score of a particular observation for the corresponding principal component.
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