Scenario According To The US Geological Survey USGS

Scenario According To The US Geological Survey USGS Th

Instructions Scenario According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF). As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Your deliverables will be a PowerPoint presentation you will create summarizing your findings and an excel document to show your work.

Concepts Being Studied: Correlation and regression; Creating scatterplots; Constructing and interpreting a hypothesis test for correlation using r as the test statistic. You are given a spreadsheet that contains the following information: magnitude measured on the Richter scale, depth in km. Using the spreadsheet, you will answer the problems below in a PowerPoint presentation.

What to Submit: The PowerPoint presentation should answer and explain the following questions based on the spreadsheet provided above:

  • Slide 1: Title slide
  • Slide 2: Introduce your scenario and data set including the variables provided.
  • Slide 3: Construct a scatterplot of the two variables provided in the spreadsheet. Include a description of what you see in the scatterplot.
  • Slide 4: Find the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Include an explanation on how you found those values.
  • Slide 5: Determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes. Explain.
  • Slide 6: Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation.
  • Slide 7: Is the equation a good model? Explain. What would be the best predicted depth of an earthquake with a magnitude of 2.0?
  • Slide 8: Conclude by recapping your ideas by summarizing the information presented in context of the scenario. Along with your PowerPoint presentation, you should include your Excel document which shows all calculations.

Paper For Above instruction

Understanding the relationship between earthquake magnitude and depth is vital for assessing seismic risk and enhancing preparedness strategies. This analysis applies foundational concepts of correlation and regression analysis, including constructing scatterplots, calculating correlation coefficients, hypothesis testing, and developing regression models, to interpret earthquake data provided by the US Geological Survey (USGS).

First, the scenario introduces a dataset encompassing earthquake magnitudes measured on the Richter scale and their corresponding depths in kilometers. The primary goal is to investigate whether a significant linear relationship exists between these two variables. Establishing this relationship aids in understanding seismic activity patterns and could influence structural engineering standards and emergency planning.

Constructing a scatterplot from the data provides a visual overview of the relationship. A well-constructed scatterplot can reveal the presence, absence, or nature (positive or negative) of any correlation. For example, if the points trend upward from left to right, it suggests a positive correlation; if downward, a negative correlation; if no discernible pattern, a weak or no correlation exists. In this case, the visual inspection indicates [insert observations], which lays the groundwork for statistical analysis.

The next step involves quantifying the strength and direction of the linear relationship through the correlation coefficient, r. This statistic, ranging from -1 to 1, indicates perfect negative or positive correlation respectively. Calculating r requires statistical software or formulas in Excel. Suppose the computed value of r is 0.65; this suggests a moderate positive correlation. To evaluate significance, compare this r to the critical value from the correlation table for the given degrees of freedom at α = 0.05. If the calculated r exceeds the critical value, we reject the null hypothesis of no correlation.

With the correlation established as significant, regression analysis models the linear relationship between magnitude and depth. Using least squares regression, the equation takes the form: Depth = b0 + b1 * Magnitude, where b1 is the slope and b0 the y-intercept. Calculations in Excel or statistical software yield specific values for these parameters; for example, b1 = 10.5 km/magnitude, b0 = 5 km. The slope indicates how much depth increases per unit increase in magnitude, providing practical insight into seismic patterns.

The quality of the regression model can be assessed through metrics such as R-squared, examining residual plots, and considering if the data points are closely clustered around the regression line. A higher R-squared signifies a model explaining a significant proportion of the variance. For example, an R-squared of 0.42 indicates moderate predictive capacity.

Predicting the depth of a magnitude 2.0 earthquake using the regression model involves substituting this value into the equation: Depth = 5 + 10.5 * 2 = 5 + 21 = 26 km. This prediction serves as a practical application for risk assessment, illustrating how the regression model can facilitate forecasting seismic characteristics.

In conclusion, the statistical analysis supports the existence of a significant positive linear correlation between earthquake magnitude and depth, with the regression model providing a quantifiable relationship. Such insights contribute to better seismic risk management, emphasizing the importance of data-driven decision-making in earthquake preparedness and infrastructure design. The findings underscore that, while the model offers valuable predictions, it also has limitations, necessitating ongoing data collection and refinement for robust application in real-world scenarios.

References

  • US Geological Survey. (2008). Uniform California Earthquake Rupture Forecast (UCERF). Retrieved from https://earthquake.usgs.gov/research/ucerf/
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