Summary: The distribution of earthquake magnitudes is right-skewed and the majority of earthquakes are distributed from 3.875 to 5.125.

Summary: The majority of the earthquake depths in this distribution are either between 0km to 225km or between 475km and 625 km, showing concentration in the higher and lower ranges.

Summary: Earthquake magnitude shows a weak negative relationship with depth.

Predict earthquake magnitude from depth.

\[ \hat{M} = \beta_0 + \beta_1 D \]

Where:

• \(\hat{M}\) = Predicted Magnitude
• \(D\) = Earthquake Depth (km)
• \(\beta_0\) = Intercept
• \(\beta_1\) = Slope

Model for Magnitude vs. Depth

\[ \hat{M} = 4.755 + (-4.31\times 10^{-4})D \]

Investigate whether earthquake magnitude has a statistically significant relationship with depth

Null Hypothesis \[ H_0: \beta_1 = 0 \] A linear relationship between depth and magnitude doesn’t exists.

Alternative Hypothesis

\[ H_1: \beta_1 \neq 0 \] A linear relationship between depth and magnitude exists.

Decision Significance Level: \(\alpha = 0.05\)

P-value: \(1.535 \times 10^{-13} < 0.05\)

Decision: Reject H₀. There is a statistically significant linear relationship.

Linear Regression Results

• Slope: ** \(-4.31 \times 10^{-4}\)
• R^2: 0.0532
• P-value: \(1.535 \times 10^{-13}\)
• Sample size: 1000 earthquakes.

Discussion

The slope indicates that earthquake magnitude tends to slightly decrease as depth increases.

\[ R^2 = 0.0532 \] Depth explains around 5.32% of the earthquake magnitude variation.

Conclusion: Although the relationship is statistically significant, depth is not a strong predictor of earthquake magnitude.