In: Statistics and Probability
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