PAF 573
YOUR NAME Elaine MacPherson
library(tidyverse)
library(stargazer)
library(GGally)
library(jtools)
# read in data
URL <- "https://raw.githubusercontent.com/spiromar/files/main/paf573/data-crime-levitt.csv"
crime <- read.csv( URL )Estimate, report, and graph the results of a regression of murder on
police in 1992. (Be sure to save your regression results to an object
with a different name.) Interpret the coefficient on
sworn.
ANSWER: The coefficient on “sworn” indicates that with each additional sworn police officer, there is an increase in murder crimes at a coefficient unit of .045. The P value is very small (.0012) which indicates the relationship is statistically significant.
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.06682 3.01534 2.344 0.0229 * sworn 0.04225 0.01234 3.423
0.0012 ** — Signif. codes: 0 ‘’ 0.001 ‘’ 0.01
‘’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.654 on 53 degrees of freedom (4 observations deleted due to missingness) Multiple R-squared: 0.1811, Adjusted R-squared: 0.1656 F-statistic: 11.72 on 1 and 53 DF, p-value: 0.0012
How likely is it that you would have observed this estimate if the
null hypothesis were actually true?
ANSWER: It would have been a .0012 % chance we would
have observed this is there were no statistic relationship (null
hypothesis).
Do the results make sense? In your opinion, what might be responsible
for the results?
ANSWER: Seeing the positive relationship implies that
with additional police officers, more murders are committed. It seems
counterintuitive that an increase in police officers would lead to more
murders, unless these two are correlated, but not causal. For example:
is there another factor that leads to both an increase in the murder
rate as well as a increase in the amount of sworn officers in cities in
the United States?
Now, let’s incorporate some additional control variables into the
model. Specifically, add the covariates listed in Table 3 of Levitt’s
paper (i.e., all but the police variable, as this is already in your
model). These are the variables you will need: x_unemp
x_welfare x_education x_a15_24
x_black x_femhea. (You will notice that the
paper uses log transformations (ln) of the variables. Don’t worry about
that for now, nor the fact that your estimates will not look the same as
Table 3. We will deal with that in the a future class.)
Why might it be important to include these particular controls in a
model of city murder rates? What are they intended to capture?
ANSWER: unemployment, education level, and poverty
disproportionately experienced by people of color are strong predictors
for crime in cities. Citing the presence of police alone as a predictive
factor in increasing or decreasing crime would not paint the whole
picture, since crime proportionately happens in cities with
proportionately more unemployment, poverty, low education levels, and
single-parent households.
With the inclusion of these control variables, the model is now a
multiple regression model. Estimate the model for 1992. Report the
regression table (using summ) and interpret the coefficient
on sworn. Be sure to comment on how likely is it that you
would have observed each estimate if the null hypothesis were actually
true.
ANSWER: The coefficient on sworn shows a .044
correlation, with a tiny P-value that is within conditional
significance. This means that there is a correlation with a tiny
likelihood (.00673) that this would be observed if the null hypothesis
were true.
How does the coefficient on sworn compare from those in
the simple univariate model? Why do they differ?
ANSWER: Singlevariate model:0.04225 coefficient with a
p-value of 0.0012 ** Multivariate model: .044573 coefficient iwth a
p-value of .00673.
it is possible that the variable of sworn officers is highly correlated with other variables we have now introduced into our analysis, such as unemployment. That could change hte coefficient on sworn officers because those two variables are interacting in some way in the regression.
Visualize the results of the 1992 results using
effect_plot. For what range of values of sworn
do you have the most confidence? For what range the least?
ANSWER: Most confidence: 30-60; lease confidence:
20-25