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Project 1 | Group 76
Joey Liu, Noemi Loera, Dale Kim
2023-10-15
library
(AER)
## Loading required package: car
## Loading required package: carData
## Loading required package: lmtest
## Loading required package: zoo
##
## Attaching package: ’zoo’
## The following objects are masked from ’package:base’:
##
##
as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: survival
data
(
"MurderRates"
)
summary
(MurderRates
$
income)
##
Min. 1st Qu.
Median
Mean 3rd Qu.
Max.
##
0.760
1.550
1.830
1.781
2.070
2.390
library
(lmtest)
library
(leaps)
library
(HH)
## Loading required package: lattice
## Loading required package: grid
## Loading required package: latticeExtra
1
## Loading required package: multcomp
## Loading required package: mvtnorm
## Loading required package: TH.data
## Loading required package: MASS
##
## Attaching package: ’TH.data’
## The following object is masked from ’package:MASS’:
##
##
geyser
## Loading required package: gridExtra
##
## Attaching package: ’HH’
## The following objects are masked from ’package:car’:
##
##
logit, vif
summary
(MurderRates
$
income)
##
Min. 1st Qu.
Median
Mean 3rd Qu.
Max.
##
0.760
1.550
1.830
1.781
2.070
2.390
hist
(MurderRates
$
income,
main =
"Income Histogram"
)
2
Income Histogram
MurderRates$income
Frequency
1.0
1.5
2.0
0
2
4
6
8
10
boxplot
(MurderRates
$
income)
3
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1.0
1.5
2.0
5
regsub
<-
regsubsets
(rate
~
.,
method =
"exhaustive"
,
nbest =
2
,
data =
MurderRates)
summaryHH
(regsub)
##
model p
rsq rss adjr2
cp
bic stderr
## 1
s 2 0.588 353 0.578 18.40 -31.4
2.90
## 2
n 2 0.560 377 0.550 22.27 -28.6
2.99
## 3
n-s 3 0.675 278 0.659
8.01 -38.1
2.61
## 4
t-n 3 0.641 308 0.623 12.88 -33.7
2.74
## 5
t-n-s 4 0.705 253 0.683
5.81 -38.6
2.51
## 6
c-n-s 4 0.698 259 0.675
6.84 -37.5
2.54
## 7
c-t-n-s 5 0.729 232 0.701
4.43 -38.5
2.44
## 8
t-i-n-s 5 0.711 247 0.682
6.89 -35.8
2.52
## 9
c-t-i-n-s 6 0.736 226 0.701
5.38 -35.9
2.44
## 10
c-e-t-n-s 6 0.730 231 0.695
6.25 -34.9
2.47
## 11
c-t-i-l-n-s 7 0.744 219 0.703
6.22 -33.5
2.43
## 12
c-e-t-i-n-s 7 0.740 223 0.697
6.88 -32.7
2.46
## 13 c-e-t-i-l-n-s 8 0.746 218 0.696
8.00 -30.0
2.46
##
## Model variables with abbreviations
##
model
## s
southernyes
## n
noncauc
## n-s
noncauc-southernyes
## t-n
time-noncauc
4
## t-n-s
time-noncauc-southernyes
## c-n-s
convictions-noncauc-southernyes
## c-t-n-s
convictions-time-noncauc-southernyes
## t-i-n-s
time-income-noncauc-southernyes
## c-t-i-n-s
convictions-time-income-noncauc-southernyes
## c-e-t-n-s
convictions-executions-time-noncauc-southernyes
## c-t-i-l-n-s
convictions-time-income-lfp-noncauc-southernyes
## c-e-t-i-n-s
convictions-executions-time-income-noncauc-southernyes
## c-e-t-i-l-n-s convictions-executions-time-income-lfp-noncauc-southernyes
##
## model with largest adjr2
## 11
##
## Number of observations
## 44
south
<-
lm
(rate
~
time
+
noncauc
+
southern,
data =
MurderRates)
summary
(south)
##
## Call:
## lm(formula = rate ~ time + noncauc + southern, data = MurderRates)
##
## Residuals:
##
Min
1Q
Median
3Q
Max
## -4.5143 -1.5177 -0.1934
1.4288
6.7320
##
## Coefficients:
##
Estimate Std. Error t value Pr(>|t|)
## (Intercept)
4.419658
1.232067
3.587 0.000901 ***
## time
-0.014227
0.007091
-2.006 0.051600 .
## noncauc
16.256184
4.719997
3.444 0.001358 **
## southernyes
3.548793
1.204250
2.947 0.005333 **
## ---
## Signif. codes:
0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
##
## Residual standard error: 2.514 on 40 degrees of freedom
## Multiple R-squared:
0.7049, Adjusted R-squared:
0.6828
## F-statistic: 31.85 on 3 and 40 DF,
p-value: 1.092e-10
#Ask for clarification when comparing the two
The Rˆ2 for (3) is 0.7459. When compared to (south), it is 0.7049. (3) has a higher Rˆ2 which indicates that
(3) is a better fit of the overall model. However, this could explain (south) to majorly be the explanatory
variable. #Ask for clarification when comparing the two 6.
region
<-
ifelse
(MurderRates
$
southern
==
"yes"
,
1
,
0
)
newReg
<-
lm
(rate
~
time
+
noncauc
+
region,
data =
MurderRates)
plot
(south,
main =
"Plot of South"
)
5
2
4
6
8
10
12
14
-4
-2
0
2
4
6
8
Plot of South
Fitted values
Residuals
lm(rate ~ time + noncauc + southern)
Residuals vs Fitted
1
37
28
6
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-2
-1
0
1
2
-2
-1
0
1
2
3
Plot of South
Theoretical Quantiles
Standardized residuals
lm(rate ~ time + noncauc + southern)
Q-Q Residuals
1
37
28
7
2
4
6
8
10
12
14
0.0
0.5
1.0
1.5
Plot of South
Fitted values
Standardized residuals
lm(rate ~ time + noncauc + southern)
Scale-Location
1
37
28
8
0.00
0.05
0.10
0.15
0.20
0.25
-2
-1
0
1
2
3
Plot of South
Leverage
Standardized residuals
lm(rate ~ time + noncauc + southern)
Cook's distance
0.5
0.5
1
Residuals vs Leverage
1
43
35
We can see that there is a pattern in the residuals, and they are portraying a cone shape. Further indicating
that the regression is heteroskedastic.
This implies that it is violating Assumption 3 of multiple linear
models: homoskedasticity.
7.
The Reset Hypothesis Test;
H
0
:
β
4
= 0
and
β
5
= 0
versus
H
1
:
β
4
̸
= 0
and/or
β
5
̸
= 0
resettest
(newReg)
##
##
RESET test
##
## data:
newReg
## RESET = 1.1266, df1 = 2, df2 = 38, p-value = 0.3347
Since the p-value is 0.3347, it is greater than the significant value
α
= 0.05. This implies that we fail to
reject the null, that our model is correctly specified.
8.
reg2
<-
lm
(rate
~
convictions
+
executions
+
time
+
income
+
lfp
+
noncauc
+
region,
data =
MurderRates)
#GQ Test to test for Heteroskedasticity
gqtest
(reg2,
point =
0.5
,
alternative=
"greater"
,
order.by =
MurderRates
$
convictions)
9
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##
##
Goldfeld-Quandt test
##
## data:
reg2
## GQ = 0.32275, df1 = 14, df2 = 14, p-value = 0.9787
## alternative hypothesis: variance increases from segment 1 to 2
#Ask which X(explanatory variable) corresponds with order.by
Since the p-value of the GQ Test is 0.9787, we fail to reject that the variances differ from the two sub-models,
implying that it is heteroskedastic.
10
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ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
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- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,

Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,