Hw8 - homework

10/15/24, 9:22 Hw 8 - homew
AM ork




Hw
8


crime <- read.delim("http://www.statsci.org/data/general/uscrime.txt")

intercept <- lm(Crime ~ 1, data = crime) #intercept model
stepwise <- lm(Crime ~., data = crime) #model with all predictors


#performing stepwise regression below
forward <- step(intercept, direction = 'forward', scope=formula(stepwise), trace = 0)

forward$anova #Viewing results of forward stepwise regression

## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 NA NA 46 6880928 561.0235
## 2 + Po1 -1 3253301.8 45 3627626 532.9352
## 3 + Ineq - 739818.6 44 2887807
1 524.2154
## 4 + Ed - 587049.8 43 2300757
1 515.5343
## 5 + M - 239404.6 42 2061353
1 512.3701
## 6 + Prob 258062.5 41 1803290
-1 508.0839
## 7 + U2 - 192233.4 40 1611057
1 504.7859

forward$coefficients #Looking at coefficients of final model

## (Intercept) Po1 Ineq Ed M Prob
## -5040.50498 115.02419 67.65322 196.47120 105.01957 -
3801.83628 ## U2
## 89.36604

Including in the variables above in our model that had significant reduction in AIC compared to intercept
only model.

backward <- step(stepwise, direction = "backward", scope=formula(stepwise), trace = 0)

backward$anova

## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 N NA 31 1354946
A 514.6488
## 2 - So 1 28.57405 32 1354974
512.6498
## 3 - Time 1 10340.669 33 1365315
84 511.0072
## 4 - LF 1 10533.159 34 1375848
02 509.3684
## 5 - 1 11674.639 35 1387523
NW 91 507.7655
## 6 - Po2 1 16706.340 36 1404229
95 506.3280
## 7 - Pop 1 22345.366 37 1426575
38 505.0700
## 8 Wealt 1 26493.246 38 1453068
- h 77 503.9349



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,10/15/24, 9:22 Hw 8 - homew
AM ork




backward$coefficients #showing coefficients of backward stepwise regression


## (Intercept) M Ed Po1 M.F
U1 ## -6426.10102 93.32155 180.12011
102.65316 22.33975 -6086.63315
## U2 Ineq
Prob ## 187.34512
61.33494 -3796.03183

#Doing both direction stepwise function
both <- step(intercept, direction = 'both', scope = formula(stepwise), trace=0)

both$anova

## Step Df Deviance Resid. Df Resid. Dev
AIC ## 1 NA NA 46
6880928 561.0235
## 2 + Po1 -1 3253301.8 45 3627626 532.9352
## 3 + Ineq -1 739818.6 44 2887807 524.2154
## 4 + Ed -1 587049.8 43 2300757 515.5343
## 5 + M -1 239404.6 42 2061353 512.3701
## 6 + Prob -1 258062.5 41 1803290 508.0839
## 7 + U2 -1 192233.4 40 1611057 504.7859

both$coefficients


## (Intercept) Po1 Ineq Ed M Pro
b
## -5040.50498 115.0241967.65322 196.47120 105.01957 -
3801.83628 ## U2
## 89.36604

This is final model coeffcients for Step wise regression. Using coefficients with reduction in AIC and low
AIC. The coefficients above are the most significant predictors according to the stepwise regression model.
Now we will do Lasso Regression on the dataset.

y <- crime %>%
select(Crime)
%>%
as.matrix()
# Response variable


#Defining matrix of predictor variables
x <- data.matrix(crime[,c('M','So','Ed', 'Po1', 'Po2', 'LF', 'M.F', 'Pop', 'NW','U1',
'U2', 'Wealth', '

y <- scale(y,scale =
TRUE) x <- scale(x,scale
= TRUE)

cv_model <- cv.glmnet(x,y, alpha = 1)

lambda1 <-
cv_model$lambda.min
lambda1

## [1] 0.0124536


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## + Fold1.Rep1: alpha=0.96599,
lambda=4.376948 ## - Fold1.Rep1:
alpha=0.96599, lambda=4.376948 ## +
Fold1.Rep1: alpha=0.11809,
lambda=0.083065 ## - Fold1.Rep1:
alpha=0.11809, lambda=0.083065 ## +
Fold1.Rep1: alpha=0.79847,
lambda=0.223218 ## - Fold1.Rep1:
alpha=0.79847, lambda=0.223218 ## +
Fold1.Rep1: alpha=0.96839,
lambda=0.073855 ## - Fold1.Rep1:
alpha=0.96839, lambda=0.073855 ## +
Fold1.Rep1: alpha=0.71521,
lambda=0.028772 ## - Fold1.Rep1:
alpha=0.71521, lambda=0.028772 ## +
Fold1.Rep1: alpha=0.86817,
lambda=0.793432 ## - Fold1.Rep1:
alpha=0.86817, lambda=0.793432 ## +
Fold1.Rep1: alpha=0.17557,
lambda=0.029739 ## - Fold1.Rep1:
alpha=0.17557, lambda=0.029739 ## +
Fold1.Rep1: alpha=0.05946,
lambda=0.001203 ## - Fold1.Rep1:
alpha=0.05946, lambda=0.001203 ## +
Fold1.Rep1: alpha=0.86951,
lambda=0.004495 ## - Fold1.Rep1:
alpha=0.86951, lambda=0.004495 ## +
Fold1.Rep1: alpha=0.09135,
lambda=4.797304 ## - Fold1.Rep1:
alpha=0.09135, lambda=4.797304 ## +
Fold1.Rep1: alpha=0.73483,
lambda=0.001937 ## - Fold1.Rep1:
alpha=0.73483, lambda=0.001937 ## +
Fold1.Rep1: alpha=0.64264,
lambda=0.942628 ## - Fold1.Rep1:
alpha=0.64264, lambda=0.942628 ## +
Fold1.Rep1: alpha=0.41315,
lambda=2.450919 ## - Fold1.Rep1:
alpha=0.41315, lambda=2.450919 ## +
Fold1.Rep1: alpha=0.89123,
lambda=1.278851 ## - Fold1.Rep1:
alpha=0.89123, lambda=1.278851 ## +
Fold1.Rep1: alpha=0.98832,
lambda=0.012198 ## - Fold1.Rep1:
alpha=0.98832, lambda=0.012198 ## +
Fold2.Rep1: alpha=0.15605,
lambda=0.398372 ## - Fold2.Rep1:
alpha=0.15605, lambda=0.398372 ## +
Fold2.Rep1: alpha=0.12382,
lambda=0.244664 ## - Fold2.Rep1:
alpha=0.12382, lambda=0.244664 ## +
Fold2.Rep1: alpha=0.74610,
lambda=0.005243 ## - Fold2.Rep1:
alpha=0.74610, lambda=0.005243 ## +
Fold2.Rep1: alpha=0.39539,
lambda=0.093521 ## - Fold2.Rep1:
alpha=0.39539, lambda=0.093521 ## +
Fold2.Rep1: alpha=0.83315,
lambda=7.311531 ## - Fold2.Rep1:
alpha=0.83315, lambda=7.311531 ## +
Fold2.Rep1: alpha=0.15201,
lambda=2.115407 ## - Fold2.Rep1:
alpha=0.15201, lambda=2.115407 ## +
Fold2.Rep1: alpha=0.26330,
lambda=0.198214 ## - Fold2.Rep1:
alpha=0.26330, lambda=0.198214 ## +
Fold2.Rep1: alpha=0.54814,
lambda=1.497670 ## - Fold2.Rep1:
alpha=0.54814, lambda=1.497670 ## +
Fold2.Rep1: alpha=0.45543,
lambda=0.259950 ## - Fold2.Rep1:
alpha=0.45543, lambda=0.259950 ## +
Fold2.Rep1: alpha=0.14076,
lambda=0.017994 ## - Fold2.Rep1:
alpha=0.14076, lambda=0.017994 ## +
Fold2.Rep1: alpha=0.96599,
lambda=4.376948 ## - Fold2.Rep1:
alpha=0.96599, lambda=4.376948 ## +

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