Lab Assignment Week 10

# Import data
setwd("C:/Users/Qiu J/Desktop/MSSP+DA 2021FALL/MSSP 897-002 Applied Linear Modeling/Assignment/Lab Assignment 10")
Arrests <- read.csv("C:/Users/Qiu J/Desktop/MSSP+DA 2021FALL/MSSP 897-002 Applied Linear Modeling/Assignment/Lab Assignment 10/Arrests.csv")
Sys.setenv(language="en")
library(psych)

Warning: package ‘psych’ was built under R version 4.1.1

describe(Arrests)

1. Create a variable called “checksbinary” that equals 1 if an arrestee’s name appears in a police database for a previous arrest, conviction, or parole and 0 if their name does not appear.

Arrests$checksbinary <- ifelse(Arrests$checks==0,0,1)

2. Create a subset of the Arrests data frame called Arrests2 that includes the following variables: checksbinary race age

Arrests2 <- subset(Arrests[,c("checksbinary","race","age")])

3. Does the age variable adhere to the assumption of linearity?

linearity <- glm(checksbinary~., family=binomial(link="logit"), data=Arrests2)
logodds <- predict(linearity)
plotlin <- with(Arrests2, data.frame(checksbinary=checksbinary, logit=logodds))
# Plotting
ggplot(plotlin, aes(x=checksbinary, y=logit))+
geom_point()+
labs(x="checksbinary", y="log odds") +
geom_smooth(method="loess", col="#3e3e3e")+
geom_smooth(method="lm", col="blue")

`geom_smooth()` using formula 'y ~ x'
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,  :
  pseudoinverse used at -0.005
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,  :
  neighborhood radius 1.005
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,  :
  reciprocal condition number  6.4089e-031
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,  :
  There are other near singularities as well. 1.01
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x else if (is.data.frame(newdata)) as.matrix(model.frame(delete.response(terms(object)),  :
  pseudoinverse used at -0.005
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x else if (is.data.frame(newdata)) as.matrix(model.frame(delete.response(terms(object)),  :
  neighborhood radius 1.005
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x else if (is.data.frame(newdata)) as.matrix(model.frame(delete.response(terms(object)),  :
  reciprocal condition number  6.4089e-031
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x else if (is.data.frame(newdata)) as.matrix(model.frame(delete.response(terms(object)),  :
  There are other near singularities as well. 1.01
`geom_smooth()` using formula 'y ~ x'

4. Estimate a logistic regression model where the checksbinary variable is regressed on race and age. Interpret the coefficient for the race variable.

lm1<-glm(checksbinary ~ race + age, family=binomial(link='logit'), data=Arrests2)
summary(lm1)

Call:
glm(formula = checksbinary ~ race + age, family = binomial(link = "logit"), 
    data = Arrests2)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.2080  -1.2014   0.6957   0.9997   1.2457  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)   
(Intercept) -0.91340    0.45213  -2.020  0.04336 * 
race         0.99701    0.30664   3.251  0.00115 **
age          0.05387    0.01914   2.815  0.00488 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 361.16  on 276  degrees of freedom
Residual deviance: 340.09  on 274  degrees of freedom
AIC: 346.09

Number of Fisher Scoring iterations: 4

lm1null<-glm(checksbinary~1, family=binomial(link='logit'), data=Arrests2)

The logit coefficient for the race variable is 0.997, which means that black arrestee has 0.997 more log odds of name appearing in a police database for a previous arrest, conviction, or parole than the white arrestee.