Question

2. The final questions relate to principal component regression (a) Based only on the eigen analysis, how many principal component variables would you use? Eigenanalysis of the Correlation Mstrix Eigenvalue 2.7015 0.7973 0.4214 0.07994 Proportion 0.675 0.199 0.100 0.020 Cumulative 0.675 0.875 0.980 1.000 (b) Using all available information, would you still use the same principal component variables? Why or why not? SEB) Z P Predictor Constant 19.6594 0.3950 49.77 0.000 PCI PC2 PC3 PC4 1.1170 0.2442 4.57 0.000 -11.5116 0.4494 25.61 0.000 -0.6886 0.6182 1.11 0.275 4.171 1.421 2.94 0.007

Answer 1

2.

a)

The number of principal component (PC) variables is dependent on the amount of variance explained by the PC variables.

From the figure it is clear that:

PC1 explains 67.5% of the total variance.

PC1 and 2 combined explain 87.5% of the total variance.

PC1,2 and 3 combined explain 98% of the total variance.

These values are obtained from the cumulative eigenvalue proportion values from the table.

From these values it seems, the first 2 PC values ( PC 1 and PC 2) explain more than 80% of the total variance which is quite sufficient.

b)

Using all the available information, it would seem that PC1, PC 2 and PC 4 have significant parameters resulting in p-values less than 5% level of significance, say. This implies that PC1, PC 2 and PC 4 are significant principal component variables, where as PC3 is not significant at 5% level of significance with p- value greater than 0.05.

This gives us an idea that although PC1 , PC 2 and PC 4 all are significant principal components. However, the majority of the total variance are explained by PC 1 and PC 2, adding PC 4 would not contribute to explanation of the variance significantly.

Hence, the answer remains the same, PC1 and PC2 should be used.