Do principal component regression on the peak flow runoff data (Exercise 5.1) to estimate the regression equation using the logarithms of all independent variables and ln(Q) as the dependent variable....

Do principal component regression on the peak flow runoff data (Exercise 5.1) to estimate the regression equation using the logarithms of all independent variables and ln(Q) as the dependent variable.

(a) Which principal components are causing a collinearity problem?

(b) Test the significance of the individual principal component regression coefficients. Which principal components will you retain for your regression?

(c) Convert the results to β⁺
_(g), compute estimates of their variances, and give the final regression equation (in terms of the Zs). (d) Compute R².

Exercise 5.1

Compute the correlation matrix for all variables including the dependent variable Q. By inspection of the correlations determine which variables are most likely to contribute significantly to variation in Q. If you could use only one independent variable in your model, which would it be?