Haun attempted to model, the mean annual discharge with 9 Cning independent vari

Question

Haun attempted to model, the mean annual discharge with 9 Cning independent variables as discussed in the lecture notes a - Discuss briefly the selection criteria presented by R^2_ady, PRESS, C_p and VLPF(VIF) Select the model(s) which would be the best to use with the optimum number of predictors and why? where R^2_ady = adjusted det. Coef PRESS = Prediction error sum C_p = Mallow's value VIF = Variance inflation factor (One variable is related to other variable (s)) 1-PRECIP, 2-Area, 3-SLOPE, 4-LENGTH, 5-perimeter, 6-Diameter, 7-shape factor, 8 - Stream frequency, 9-Relief Ratio R^adj = [^(n - 1)/(n- (p+1)) SSE/SSY] S_y = SSy/(n - 1) = sigma(y_i - y^bar)^2/(n - 1) S_e = SSE/(n - d) = sigma(y_i - y circ_i)^2/(n - v) PRESS = sigma e_i^2 = z(y_i - y circ_i)^2 Mallows C_p = [p + (n - p)(s_p^2 - sigma^2)/sigma^2] where m = (p+1) = v S_p^2 = MSE sigma^2 = VIF = [1/(1 - R_j^2)] rArr influence factor for variable j

Explanation / Answer

a)

Variables with VIF > 3.3 are said have multi-co-linearity associated with them. Hence on basis of this criteria I can say that model with total number of independent variables 2 or 3 is compatible with VIF criteria.

Adjusted R^2 increases with addition of significant variables. Hence I prefer model with 3 independent variables.

b)

On basis of above criteria’s I can say that I prefer model with 3 independent variables.

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