Analysis of Age, Income, and Crime: Correlation and Regression

This assignment focuses on bivariate correlation and regression analysis within a sociological context, specifically examining the relationship between the age of convicted drug offenders and their monthly income earned in illegal drug markets. The solution addresses key concepts such as identifying independent and dependent variables, determining their measurement scales (nominal, ordinal, interval, ratio), and interpreting the Pearson's r correlation coefficient. It explains the direction and magnitude of the relationship between age and income, calculates and interprets the coefficient of determination, and analyzes the regression equation to understand the regression slope coefficient and predict income based on age. The assignment also includes hypothesis testing involving two and three population means, including the relationship between impulsivity and criminal offending and the relationship between prison security levels and the number of prior offenses. The solutions provide detailed explanations and calculations to support the analysis of the provided data.

Chapter 12: Bivariate Correlation and Regression
1. You want to study the relationship between age of convicted drug offenders (in years) and monthly
income (in dollars) earned in illegal drug markets. Your hypothesis is that older offenders earn more
money. A scatter plot is provided for data examining this relationship in a sample of 15 youthful
offenders.
a) What are the independent and dependent variables in your study? How are they measured (nominal,
ordinal, interval, ratio)?
Answer: IV: Age – Ratio
DV: Monthly Income (in dollars) - Ratio
b) “Pearson’s r correlation coefficient” for the relationship between age and income is .78. In your own
words, explain what this tells us about the relationship (e.g., direction, magnitude) between these two
variables.
Answer: The correlation coefficient of 0.78 indicates that there is a strong and positive relationship
between age and income. In other words, a one year increase in age will lead to $0.78 increase in the
monthly income of the individual.
c) Calculate and the “coefficient of determination”. Interpret it
Answer: r2 = 0.782= 0.6084
Interpretation: The coefficient of determination indicates that 60.84% of the variations in
monthly income can be explained by age.
2. Assume you have conducted a bivariate regression analysis. The following represents your regression
equation, where Y = Income (in dollars) and X = Age (in years).
y = -4,875 + 275x
a) Interpret the “regression slope coefficient”
Answer: The regression slope coefficient means that for each year increase in Age, there is an increase of
$275 in income.

b) Based on this equation, how much money would you expect a 30 year-old drug offender to earn?
Answer: y=−4,875+(275∗30) = y=−4,875+8,250 = $3,375