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data(USStates)
States <- USStates

States$Clinton <- abs(as.numeric(States$Elect2016) - 2)
table(States$Clinton)
## 
##  0  1 
## 30 20
head(States[, c("State", "Clinton", "College", "ClintonVote")])
##        State Clinton College ClintonVote
## 1    Alabama       0    26.0       34.36
## 2     Alaska       0    26.5       36.55
## 3    Arizona       0    27.4       45.13
## 4   Arkansas       0    24.7       33.65
## 5 California       1    34.5       61.73
## 6   Colorado       1    39.6       48.16

TASK 1

m1 <- lm(ClintonVote ~ College + HouseholdIncome + NonWhite, data = States)
summary(m1)
## 
## Call:
## lm(formula = ClintonVote ~ College + HouseholdIncome + NonWhite, 
##     data = States)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.697  -3.605  -1.036   4.495  13.686 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      0.99082    6.01413   0.165    0.870    
## College          1.12498    0.22514   4.997 8.88e-06 ***
## HouseholdIncome -0.07554    0.15345  -0.492    0.625    
## NonWhite         0.43123    0.08246   5.230 4.05e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.622 on 46 degrees of freedom
## Multiple R-squared:  0.6155, Adjusted R-squared:  0.5904 
## F-statistic: 24.55 on 3 and 46 DF,  p-value: 1.237e-09
tab_model(m1,show.ci=FALSE, show.se=TRUE, show.stat=TRUE)
  ClintonVote
Predictors Estimates std. Error Statistic p
(Intercept) 0.99 6.01 0.16 0.870
College 1.12 0.23 5.00 <0.001
HouseholdIncome -0.08 0.15 -0.49 0.625
NonWhite 0.43 0.08 5.23 <0.001
Observations 50
R2 / R2 adjusted 0.616 / 0.590

TASK 2

m2 <- lm(ClintonVote ~ College + HouseholdIncome + NonWhite + Region, data = States)
summary(m2)
## 
## Call:
## lm(formula = ClintonVote ~ College + HouseholdIncome + NonWhite + 
##     Region, data = States)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.3217  -4.1695   0.0435   4.2880  11.2477 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     14.80589    7.15877   2.068   0.0447 *  
## College          1.18862    0.25668   4.631 3.36e-05 ***
## HouseholdIncome -0.42863    0.17107  -2.506   0.0161 *  
## NonWhite         0.52461    0.08175   6.417 9.03e-08 ***
## RegionNE         8.03052    2.72062   2.952   0.0051 ** 
## RegionS         -3.40381    2.74204  -1.241   0.2212    
## RegionW          5.65798    2.77249   2.041   0.0474 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.82 on 43 degrees of freedom
## Multiple R-squared:  0.7224, Adjusted R-squared:  0.6836 
## F-statistic: 18.65 on 6 and 43 DF,  p-value: 1.545e-10
AIC(m1,m2)
##    df      AIC
## m1  5 336.7667
## m2  8 326.4857
BIC(m1,m2)
##    df      BIC
## m1  5 346.3268
## m2  8 341.7819
m3 <- list("M1" = m1, "M2" = m2)
modelsummary(m3, fmt = 2, statistic = "std.error")
tinytable_3hzwy30m1745ym7kard9
M1 M2
(Intercept) 0.99 14.81
(6.01) (7.16)
College 1.12 1.19
(0.23) (0.26)
HouseholdIncome -0.08 -0.43
(0.15) (0.17)
NonWhite 0.43 0.52
(0.08) (0.08)
RegionNE 8.03
(2.72)
RegionS -3.40
(2.74)
RegionW 5.66
(2.77)
Num.Obs. 50 50
R2 0.616 0.722
R2 Adj. 0.590 0.684
AIC 336.8 326.5
BIC 346.3 341.8
Log.Lik. -163.383 -155.243
RMSE 6.35 5.40

TASK3

m.interact <- lm(ClintonVote ~ College + NonWhite + College:NonWhite, data=States)
summary(m.interact)
## 
## Call:
## lm(formula = ClintonVote ~ College + NonWhite + College:NonWhite, 
##     data = States)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.446  -3.543  -0.295   3.936  13.831 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      -15.22574   13.26349  -1.148 0.256927    
## College            1.50058    0.39913   3.760 0.000479 ***
## NonWhite           0.99725    0.47769   2.088 0.042397 *  
## College:NonWhite  -0.01802    0.01457  -1.236 0.222664    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.532 on 46 degrees of freedom
## Multiple R-squared:  0.6259, Adjusted R-squared:  0.6015 
## F-statistic: 25.66 on 3 and 46 DF,  p-value: 6.636e-10
library(effects)
interaction_plot <- effect("College*NonWhite", m.interact, xlevels=list(College=seq(0, 100, 10), NonWhite=seq(0, 100, 10)))
plot(interaction_plot, main="Interaction Effect of College and NonWhite on ClintonVote", xlab="% College Educated", ylab="% Clinton Vote")

TASK4:

States$ClintonWin <- ifelse(States$ClintonVote > 50, 1, 0)
head(States)
##        State HouseholdIncome Region Population EighthGradeMath HighSchool
## 1    Alabama          46.472      S      4.875           268.7       87.1
## 2     Alaska          76.114      W      0.740           274.3       92.8
## 3    Arizona          53.510      W      7.016           279.9       87.1
## 4   Arkansas          43.813      S      3.004           274.4       89.1
## 5 California          67.169      W     39.537           275.6       87.4
## 6   Colorado          65.458      W      5.607           284.7       91.5
##   College    IQ    GSP Vegetables Fruit Smokers PhysicalActivity Obese NonWhite
## 1    26.0  95.7 40.279       80.7  55.1    20.9             42.8  36.2     31.6
## 2    26.5  99.0 70.936       81.0  63.1    21.0             58.3  29.5     34.7
## 3    27.4  97.4 43.096       79.2  62.8    15.6             52.7  29.5     22.5
## 4    24.7  97.5 38.467       80.7  55.3    22.3             45.4  37.1     22.7
## 5    34.5  95.5 67.698       78.6  67.5    11.3             57.5  25.8     39.4
## 6    39.6 101.6 59.057       82.6  67.0    14.6             58.7  23.0     15.8
##   HeavyDrinkers Electoral ClintonVote Elect2016 TwoParents StudentSpending
## 1          5.45         9       34.36         R       60.9           9.236
## 2          7.33         3       36.55         R       71.5          17.510
## 3          5.57        11       45.13         R       62.7           7.613
## 4          5.32         6       33.65         R       63.3           9.846
## 5          5.95        55       61.73         D       66.8          11.495
## 6          7.30         9       48.16         D       71.9           9.575
##   Insured Clinton ClintonWin
## 1    83.7       0          0
## 2    80.2       0          0
## 3    83.4       0          0
## 4    84.1       0          0
## 5    85.2       1          1
## 6    87.2       1          0
m.logit <- glm(ClintonWin ~ College + HouseholdIncome + Region, data=States, family=binomial(link="logit"))
summary(m.logit)
## 
## Call:
## glm(formula = ClintonWin ~ College + HouseholdIncome + Region, 
##     family = binomial(link = "logit"), data = States)
## 
## Coefficients:
##                   Estimate Std. Error z value Pr(>|z|)   
## (Intercept)      -17.16240    6.31603  -2.717  0.00658 **
## College            0.28494    0.14633   1.947  0.05150 . 
## HouseholdIncome    0.07628    0.07376   1.034  0.30110   
## RegionNE           2.17592    1.40578   1.548  0.12166   
## RegionS          -16.31016 2420.64651  -0.007  0.99462   
## RegionW            2.58895    1.62430   1.594  0.11096   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 57.306  on 49  degrees of freedom
## Residual deviance: 25.780  on 44  degrees of freedom
## AIC: 37.78
## 
## Number of Fisher Scoring iterations: 18
modelsummary(m.logit, fmt = 2, statistic = "std.error")
tinytable_rgzfz09iz5iewse0g6a3
(1)
(Intercept) -17.16
(6.32)
College 0.28
(0.15)
HouseholdIncome 0.08
(0.07)
RegionNE 2.18
(1.41)
RegionS -16.31
(2420.65)
RegionW 2.59
(1.62)
Num.Obs. 50
AIC 37.8
BIC 49.3
Log.Lik. -12.890
RMSE 0.29 
tab_model(m.logit,show.ci=FALSE, show.se=TRUE, show.stat=TRUE)
  ClintonWin
Predictors Odds Ratios std. Error Statistic p
(Intercept) 0.00 0.00 -2.72 0.007
College 1.33 0.19 1.95 0.052
HouseholdIncome 1.08 0.08 1.03 0.301
Region [NE] 8.81 12.39 1.55 0.122
Region [S] 0.00 0.00 -0.01 0.995
Region [W] 13.32 21.63 1.59 0.111
Observations 50
R2 Tjur 0.564

TASK5:

effect_plot <- allEffects(m.logit)
plot(effect_plot)

plot_model(m.logit, type = "eff", terms = c("College", "HouseholdIncome", "Region"))