Bivariate Correlation and Regression Answer 2022

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.