Crime Rate and Cell Phones The linear correlation between violent crime rate and percentage of the population that has a cell phone is −0.918 for years since 1995. Do you believe that increasing the percentage of the population that has a cell phone will decrease the violent crime rate? What might be a lurking variable between percentage of the population with a cell phone and violent crime rate?

Verified step by step guidance

1. Step 1: Understand the meaning of the correlation coefficient. A correlation of −0.918 indicates a strong negative linear relationship between the percentage of the population with a cell phone and the violent crime rate. This means that as one variable increases, the other tends to decrease.
2. Step 2: Interpret the correlation carefully. While a strong negative correlation suggests an association, it does not imply causation. Therefore, we cannot conclude that increasing cell phone usage directly causes a decrease in violent crime rate.
3. Step 3: Consider the possibility of lurking variables. A lurking variable is an unobserved factor that influences both variables, potentially explaining the observed correlation without a direct causal link.
4. Step 4: Identify potential lurking variables. For example, socioeconomic factors, improvements in law enforcement, or technological advancements over time could affect both cell phone adoption and crime rates.
5. Step 5: Conclude that to establish causation, further analysis such as controlled experiments or more detailed observational studies would be necessary, rather than relying solely on correlation.

Key Concepts

Correlation Coefficient

The correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1. A value of -0.918 indicates a strong negative correlation, meaning as one variable increases, the other tends to decrease. However, correlation does not imply causation, so this relationship alone does not prove that one variable causes changes in the other.

Causation vs. Correlation

Causation means one variable directly affects another, while correlation only indicates a relationship without proving cause. Even a strong correlation can be due to coincidence or other factors. It is important to avoid assuming that increasing cell phone usage causes a decrease in violent crime without further evidence or experimental data.

Lurking Variables

A lurking variable is an unobserved factor that influences both variables being studied, potentially explaining their correlation. For example, economic development or urbanization might affect both cell phone adoption and crime rates. Identifying lurking variables helps avoid misleading conclusions about direct relationships between variables.