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In: Statistics and Probability

I already ran PCA on data given in last Principal Component Analysis: Energy_kcal, Protein_g, Fat_g, Carb_g...

I already ran PCA on data given in last

Principal Component Analysis: Energy_kcal, Protein_g, Fat_g, Carb_g

Eigenanalysis of the Correlation Matrix

Eigenvalue 2.2504 1.1894 0.5583 0.0018
Proportion 0.563 0.297 0.140 0.000
Cumulative 0.563 0.860 1.000 1.000


Variable PC1 PC2 PC3 PC4
Energy_kcal 0.663 0.090 -0.028 -0.743
Protein_g 0.399 -0.578 0.663 0.261
Fat_g 0.604 0.027 -0.563 0.564
Carb_g 0.191 0.811 0.494 0.250

I ned answers to these two parts

State principal components as linear combination of given set of variables.

Explain how you will compute scores selecting one of the components.

Data

Energy_kcal   Protein_g   Fat_g   Carb_g
333.75   23.38   29.23   2.44
387.19   27.95   34.45   0.40
306.56   18.80   29.03   0.54
349.69   22.95   32.25   0.75
281.25   20.78   23.81   2.41
298.13   20.25   26.25   2.72
238.13   22.74   16.96   3.05
282.19   23.04   21.01   7.00
345.00   21.95   32.00   1.23
237.19   8.58   24.27   3.95
393.75   26.64   29.66   15.32
367.50   33.52   27.51   3.55
330.00   22.29   30.04   0.63
329.06   23.98   28.36   2.36
163.13   10.56   13.83   3.35
129.38   10.68   8.43   5.66
362.81   29.81   28.70   4.00
345.94   20.19   32.64   2.20
356.25   25.25   29.61   5.92
318.75   22.88   27.67   2.07
343.13   17.00   32.71   5.26
351.56   20.75   33.23   1.90
313.13   23.18   26.64   2.31
310.31   18.43   26.06   7.86
309.38   15.81   27.30   8.08
337.04   22.87   25.71   4.25
302.61   17.12   22.61   8.24
135.65   3.09   13.14   4.06
203.48   2.82   22.07   3.46
304.70   2.26   35.33   2.80
360.00   2.14   42.29   2.63
268.17   3.34   25.39   11.80
140.87   3.07   13.71   4.02
201.39   2.16   22.55   2.72
91.83   4.75   4.79   7.60
185.74   3.39   18.94   4.42
65.74   3.47   3.95   4.48
65.74   3.47   3.89   4.48
131.48   21.97   0.00   9.95
568.70   5.00   40.55   51.83

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