How attempted to model, the mean annual discharge with independent variables as

Question

How attempted to model, the mean annual discharge with independent variables as discussed in the lecture notes a. Discuss briefly the selection criteria presented by R^_ady, Press, C_0 VLPP (VIF) b. Select the model(s) which would be the best to use with the optimum number of predictors only why? where R_ady^2 = adjusted det coefficient PRESS = Prediction error sum C_p = Mallow's value VIF = Variance inflation factor (one variable is related to other variable(s)) 4-PRECIR, 2 - Anea, 3- SLOPE 4- LENGTH 6- Perimeter, 6 - Diameter 7- shape factor, 8 - stream frequency 9 - relief Ratio R_adj^2 = [(n - 1)/[(n - (p + 1) SSE/SSY] S_y = SSY/(n - 1) = sigma (y_i - y)^2/(n - 1) S_e = SSE/(n - v) = sigma (y_i - y_j^2)/(n - v) PRESS = sigma e_j^2 = Z(y_i - y_i)^2 Mallows C_p = [P + (n - n)(s_p^2 - delta y/sigma^2] where VIF_j = [1/(- R_j^2)] influence factor for j

Explanation / Answer

a) The selection criteria depends on the type and nature of the variables to analize. A random sample selection it´s the most common and is used for independent variables. In this particular case, the variables shows prediction measures, the objective is to find the best and precise measure model.

b) The best model of prediction will be depend on the kind of variable is and what measure could give. If the variable is cuantitative, one of the best models is the multiple regression, indicates how much influence have the independent variable on the dependent one, and why, also, gives the difference between the variables like means, std. desviation, variance, between others. By other hand, if we have at least one cualitative variable, we can use the logit model that explains the function of all the variables based on probabilities.

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