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ISYE 6501 Introduction to Analytic Model Homework 5 Georgia Institute of Technology.
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ISYE 6501 Introduction to Analytic Model Homework 5 Georgia Institute of Technology.
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ISYE 6501 Introduction to AnalyticModel Homework 5 Georgia
Institute of Technology.
, lOMoARcPSD| 43283024
isye6501_homework5
2024-06-19
Question 11.1
1) Backward Elimination
The backward elimination process started with all predictor variables and iteratively removed the least
significant variables based on the Akaike Information Criterion (AIC). The final model after backward
elimination includes the following predictors:
M Ed Po1 M.F U1 U2 Ineq Prob
The AIC for this model was 503.93.
Forward Selection The forward selection method also started with all predictor variables and included vari-
ables iteratively to minimize the AIC. The final model selected by forward selection contains the same
variables as the backward elimination model.
Stepwise Selection The stepwise selection method combined both forward and backward selection procedures
to minimize the AIC. The final model from stepwise selection included:
M Ed Po1 M.F U1 U2 Ineq Prob
This model also had an AIC of 503.93, identical to the backward and forward models.
2) LASSO (Least Absolute Shrinkage and Selection Operator)
LASSO was used to perform variable selection and regularization to enhance the prediction accuracy and
interpretability of the statistical model. The standardized predictors (x) and the standardized response
(y) were used in the model. The glmnet package was used to fit the LASSO model, and cross-validation
(cv.glmnet) was performed to select the optimal lambda that minimized the mean cross-validated error.
After plotting the LASSO path and selecting the optimal lambda using cross-validation, the coefficients of
the final model can be extracted. The significant predictors typically shrink towards zero with LASSO,
leading to a simpler model with fewer predictors.
Based on the model selection procedures (backward elimination, forward selection, and stepwise selection),
the significant predictors for the crime rate are:
M Ed Po1 M.F U1 U2 Ineq Prob
3) ELASTIC NET
The output of the provided R script indicates that the Elastic Net model was tuned and evaluated for
different values of the mixing parameter alpha to identify the best performing model based on the mean
squared error. Train the data with cross-validation then evaluated it on test data. Then I identified the best
model by detecting the lowest MSE which was when Alpha = 0.8
, lOMoARcPSD| 43283024
rm(list=ls())
set.seed(123)
data <- read.table("uscrime.txt", stringsAsFactors = FALSE, header = TRUE)
backwards_model <- lm(Crime~., data=data)
backwards_model <- step(backwards_model, direction ="backward")
## Start: AIC=514.65
## Crime ~ M + So + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 +
## U2 + Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - So 1 29 1354974 512.65
## - LF 1 8917 1363862 512.96
## - Time 1 10304 1365250 513.00
## - Pop 1 14122 1369068 513.14
## - NW 1 18395 1373341 513.28
## - M.F 1 31967 1386913 513.74
## - Wealth 1 37613 1392558 513.94
## - Po2 1 37919 1392865 513.95
## <none> 1354946 514.65
## - U1 1 83722 1438668 515.47
## - Po1 1 144306 1499252 517.41
## - U2 1 181536 1536482 518.56
## - M 1 193770 1548716 518.93
## - Prob 1 199538 1554484 519.11
## - Ed 1 402117 1757063 524.86
## - Ineq 1 423031 1777977 525.42
##
## Step: AIC=512.65
## Crime ~ M + Ed + Po1 + Po2 + LF + M.F + Pop + NW + U1 + U2 +
## Wealth + Ineq + Prob + Time
##
## Df Sum of Sq RSS AIC
## - Time 1 10341 1365315 511.01
## - LF 1 10878 1365852 511.03
## - Pop 1 14127 1369101 511.14
## - NW 1 21626 1376600 511.39
## - M.F 1 32449 1387423 511.76
## - Po2 1 37954 1392929 511.95
## - Wealth 1 39223 1394197 511.99
## <none> 1354974 512.65
## - U1 1 96420 1451395 513.88
## - Po1 1 144302 1499277 515.41
## - U2 1 189859 1544834 516.81
## - M 1 195084 1550059 516.97
## - Prob 1 204463 1559437 517.26
## - Ed 1 403140 1758114 522.89
## - Ineq 1 488834 1843808 525.13
##
2
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