Assume two models were developed using 50 data points (n=50). The models and the
ID: 3301113 • Letter: A
Question
Assume two models were developed using 50 data points (n=50). The models and their respective ANOVA tables are given below Model1: Let's considerthe regression model, which we will referto as Model1, given by Y= 10,000 + 150* X1 25*X1^2 + 60*X2 (M1) Analysis of Variance Table for Fitted Regression Model Sum of Squares from the Regression Sum of Squares for the ErrOr Total Sum SSR SSE SST 750 250 1000 Model2: Now let's consider an alternate regression model, which we will referto as Model 2, given by Y= 9,750 + 145* X1 +75*X2 (M2) Analysis of Variance Table for Fitted Regression Model Sum of Squares from the Regression Sum of Squares for the ErrOr Total Sum of Squares SSR SSE SST 725 275 1000 Assignment: Research the formula for the following metrics. Also, determine how to interpretthe results. .Adjusted R-Squared Akaike Information Criteria (AIC) Akaike Information Criteria with correction for sample size (AICC) . Schwarz Information Criteria (BIC, SBC) Using the information given for M1 and M2, calculate (by hand or using EXCEL) the Adjusted R Squared, AIC, SBC, and AICC for both models (M1 and M2). Simple, right? OK, here's the catch. You need to calculate the values AND comment on them (1 or 2 sentences should suffice). I just need to know that you know what these metrics are and how to use them.Forexample, you might say. . "Using Adjusted R-Squared, I would prefer Model M1 because" . "Using AIC, I would prefer Model M2 because...."Explanation / Answer
The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squaredincreases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance. more value of it is desirable.
Adjusted R-square=1-(SSE/(n-p))/(SST/(n-1))
here n=50 and p=4
Adjusted R-square for M1 is =1-(250/(50-4))/(1000/(50-1))=0.7337
Adjusted R-square for M2 is =1-(275/(50-4))/(1000/(50-1))=0.7071
using adjusted R-square , I would prefer Model M1 because its value is more than M2
The Akaike information criterion (AIC) is a measure of the relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Hence, AIC provides a means for model selection.
It offers a relative estimate of the information lost when a given model is used to represent the process that generates the data. In doing so, it deals with the trade-off between the goodness of fit of the model and the complexity of the model.
AIC = 2k + nln(RSS/n)
for M1, AIC=2*4+50*log(250/50)=42.95
for M2, AIC = 2*4+50*log(275/50)=45.01
M1 is better model
Given a set of candidate models for the data, the preferred model is the one with the minimum AIC value.