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Criminal justice agencies are often interested in determining whether certain characteristics or variables of offenders can predict certain outcomes. For instance,
recidivism
, which is defined as returns to prison after being released, is often looked at in terms of what variables predict that outcome. Variables such as race, gender, criminal history, treatment received, and others can influence recidivism.
For this Individual Project, you are working as an analyst for a State Correctional Agency. You have been asked to investigate whether or not the number of drug arrests an individual has predicts his or her number of prison incarcerations. These data will be used to shape a sentencing policy.
This assignment will require you to complete the linear regression using Microsoft Excel and to interpret the results of that analysis. Before you do that, watch the following video and Web site on residuals and residual plots because there will be questions about this later:
Residual Plots
Web site:
Residual Analysis in Regression
Transfer the data from the following table into Microsoft Excel. Then, use the data analysis part of Excel to conduct the regression (follow the steps below).
SUBJECT
# DRUG ARRESTS (X)
# PRISON INCARCERATIONS (Y)
Steps to conduct regression in Excel:
Cut and paste these columns of data into an Excel sheet.
Go to the Data tab, and click the Data Analysis button to open the dialogue window. Highlight “Regression,” and click “OK.” This tells Excel that you will be calculating a regression model.
When the Regression dialogue opens, it will require inputs. First, click in the Input Y Range box, and then use your cursor to select all of your values that are in the Y column. This tells Excel what data to consider the response variable. Make sure the dotted line encompasses the entire column to include the label header (# prison incarcerations).
Next, click Input X Range box, and select all of the values that are in the X column. This tells Excel which data to consider your explanatory variable. Again, make sure the dotted line encompasses all of the column to include the header (# drug arrests).
Next, click the Labels box that says and then the New Worksheet Ply button, and Type “Output” in the box next to that button. This tells Excel to read the labels of your columns as names and not data and to place the output of the analysis on a new worksheet.
Then, click the Residuals box and the Residual Plots box. This tells Excel to analyze the residuals for the regression line and to plot them on a graph, giving you a visual idea of how far away each point of your data is from the predicted values given by the regression equation.
Once done, click “OK” to run the analysis.
Now that you have conducted the analysis, answer the following questions:
What is the R-square value for the regression model?
What does the R-square value tell you about the regression model?
What is the significance F value of the model?
What does the significance F value tell you about the statistical significance of the model?
What is the coefficient (t stat value) for the X-variable drug arrests?
What does the coefficient (t stat value) mean? In other words, how do you interpret the coeffficient?
What is the p-value for the X variable drug arrests?
What does the p-value for drug arrests tell you about its ability to predict prison incarcerations at a level of statistical significance?
Is the residual plot a random pattern, nonrandom U pattern, or an inverse U pattern?
What does the type of pattern tell you about the “fit†of the regression model to the data?
Residual plots
[Video file]. Retrieved from https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/assessing-fit-least-squares-regression/v/residual-plots
Stat Trek. (2017).
Residual analysis in regression.
Retrieved from http://stattrek.com/regression/residual-analysis.aspx?Tutorial=AP plus references
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