📊 Exploring Police Killings and City Size

We’ll explore whether there’s a relationship between the size of a city and the number of people killed by police using real-world data from the 100 largest U.S. cities.

🔍 The Data

Here’s a random sample of five cities with their 2015 population (in 100,000s) and number of deaths by law enforcement (2013–2019):

Birmingham, AL – 2.12 → 7 deaths
Jacksonville, FL – 8.68 → 39 deaths
Norfolk, VA – 2.46 → 11 deaths
Omaha, NE – 4.44 → 15 deaths
Stockton, CA – 3.06 → 18 deaths

📈 Question 1: What is the regression equation for this sample?

Show Answer

The regression line is approximately: y = -2.07 + 4.87x

Correlation coefficient (r) ≈ 0.97 → strong positive linear relationship.

Coefficient of determination (r²) ≈ 0.94 → 94% of the variation in deaths is explained by population size.

💬 What does that tell us?

Show Answer

Bigger cities tend to have more deaths by police. The relationship is strong and linear.

🤔 What does r² actually mean?

Show Answer

r² = 0.94 means 94% of the variation in deaths is predicted by city size. The remaining 6% is from other factors or random variation.

🔁 Try a Different Sample

Here’s a new sample:

Charlotte, NC – 8.27 → 21 deaths
Chula Vista, CA – 2.66 → 2 deaths
Lubbock, TX – 2.49 → 3 deaths
Portland, OR – 6.32 → 18 deaths
Seattle, WA – 6.84 → 23 deaths

📈 Question 2: What is the regression equation for this new sample?

Show Answer

The regression line is approximately: y = -5.75 + 4.23x

r ≈ 0.93 → still a strong positive correlation

r² ≈ 0.87 → about 87% of the variation in deaths is explained by population

💬 Do the results support the same conclusion?

Show Answer

Yes. Both samples show a strong positive relationship between city size and police-related deaths.

🧪 Why do we test multiple samples?

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Using multiple samples checks if the relationship is consistent. If it is, we can feel more confident that the correlation is real and not due to random chance.

⚠️ Final Note: Does this prove causation?

Show Answer

Nope. Correlation does not mean causation. There could be other factors involved — like local policies, demographics, or reporting methods. We’re just seeing a strong statistical association here.