The following table gives the error sum of squares (SSE) values from fitting mul
ID: 3293187 • Letter: T
Question
The following table gives the error sum of squares (SSE) values from fitting multiple regression models on a data set of size n = 356 that involves a continuous response Y and three predictors (X_1 X_2 continuous and X_3 categorical with 4 leveks). Assuming that an intercept term is always included in all candidate models under our consideration, compute their corresponding AIC and BIC measures respectively and identify the best model accordingly. Note that AIC and BIC are up to some irrelevant constant, given by AIC = n middot ln (SSE) + 2 times p BIC = n middot ln(SSE) + ln(n) times p where p is the number of slope coefficients in the model. Identify the 'best' model according to AIC and BIC.Explanation / Answer
Using the given formula of AIC & BIC we find out the AIC & BIC values. Here the column p is the no of estimable parameters in the given candidate models. Like for the first model with only X1, no of parameters is 1+1=2.[Since one for the intercept term & one for the coefficient of X1. Hence two parameters are there.Similarly for the other models.]
SSE p n AIC BIC
332.53 2 356 2071.20 2078.95
231.89 2 1942.87 1950.62
226.34 2 1934.25 1942.00
158.86 3 1810.22 1821.84
89.45 3 1605.75 1617.37
96.66 3 1633.35 1644.97
87.34 4 1599.25 1614.75
From the above values of AIC & BIC we can see that the last model has got least AIC and BIC. i.e the model with X1,X2,X3. Hence that is the best model according to the AIC BIC criterion. Moreover adding to that the last model has got least SSE among all which indicates that the SSR i.e sum of squares due to regression is high which explains that the 3 variables X1,X2,X3 well explains the model.Hence the result.
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