Over the last 10 years, tornadoes have caused the highest number of fatalities among natural hazards in the United States. In this study, a multivariate regression model is presented to assess the expected number of injuries caused by a tornado as a function of tornado intensity and the tornado path length.
December 10,2020
Introduction
Research Question
Is the magnitude and path length of tornadoes predictive of the injuries caused by them?
Data
NOAA’s Storm Events Database is an integrated database of severe weather events across the United States from 1950 to this year, with information about a storm event’s location, azimuth, distance, impact, and severity, including the cost of damages to property and crops. The database is hosted on Google BigQuery and is publicly available.
Data
Each case represents a tornado that hit the U.S. after 1950. There are 16000 observations in our dataset.
## Rows: 16,000 ## Columns: 15 ## $ storm_date <chr> "2015-06-07", "2015-11-11", "2016-09-21", "2008-… ## $ storm_time <chr> "00:15:00", "14:00:00", "17:32:00", "17:59:00", … ## $ magnitude <chr> "0", "1", "0", "2", "2", "2", "2", "1", "2", "0"… ## $ injured_count <int> 0, 0, 0, 0, 0, 30, 1, 0, 15, 0, 0, 0, 0, 0, 0, 0… ## $ fatality_count <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, … ## $ property_loss <dbl> 0.015, 0.405, 3000.000, 0.510, 75000.000, 12.000… ## $ crop_loss <dbl> 4.00e-03, 0.00e+00, 3.00e+03, 0.00e+00, 1.00e+04… ## $ yearly_tornado_count <int> 575683, 602617, 614379, 553, 615497, 356, 1204, … ## $ start_lon <dbl> -94.0213, -94.5585, -92.7308, -96.3000, -94.7771… ## $ start_lat <dbl> 42.0995, 40.7157, 42.9155, 43.1400, 40.5851, 41.… ## $ end_long <dbl> -93.9673, -94.3545, -92.7105, -96.4200, -94.6462… ## $ end_lat <dbl> 42.1081, 40.9904, 42.9341, 43.3000, 40.6043, 41.… ## $ length <dbl> 2.83, 21.80, 1.65, 12.95, 6.99, 4.50, 12.00, 1.0… ## $ width <dbl> 120, 1350, 150, 1200, 3000, 1761, 300, 450, 2640… ## $ tornado_path_geom <chr> "LINESTRING(-94.0213 42.0995, -93.9673 42.1081)"…
Exploring the dataset
Storms Per Year
The dataset was filtered to only include data from 2007 onward.
Exploring the dataset
Injuries due to Tornadoes by Year
Predicting Injuries from Tornadoes
Dependent Variable: Injured_Count: Number of people injured as a result of the storm
Independent Variables:
Magnitude: EF-Scale rating for the tornado. Possible values are 0, 1, 2, 3, 4 , 5 and unknown.
Length:Length of the tornado, in miles
Dummy Coding
Converted ‘Magnitude’ to indicate if its high(1) or low()
Testing for collinearity between the independent variables
The correlation between magnitude and length, although moderate, seem to be statistically significant. However, since ‘Magnitude’ is a dichotomous variable, is it accurate to do a correlation between the independent variables in this case?
Regression Model
m_injury <- lm(injured_count ~ length + magnitude, data = Tornado3) summary(m_injury)
## ## Call: ## lm(formula = injured_count ~ length + magnitude, data = Tornado3) ## ## Residuals: ## Min 1Q Median 3Q Max ## -84.19 -1.06 1.13 1.89 1427.17 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -2.17122 0.38144 -5.692 1.31e-08 *** ## length 0.68550 0.04651 14.738 < 2e-16 *** ## magnitude 19.69801 1.89944 10.370 < 2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 25.99 on 6003 degrees of freedom ## (36 observations deleted due to missingness) ## Multiple R-squared: 0.09545, Adjusted R-squared: 0.09514 ## F-statistic: 316.7 on 2 and 6003 DF, p-value: < 2.2e-16
Predicted Injury Count = -2.21774+0.68(length)+24.75521(magnitude)
The predicted injury count increases by about 19.7% as if the magnitude of the storm is above 3 and increases by 0.68% with tornadoes that are longer. Adjusted R2 is 0.09514 which means that 9% of the variance is explained by length and magnitude of the tornado are longer in miles.
Forward Selection
I will add the width variable to see if it improves our adjusted r2.
m_injury2 <- lm(injured_count ~ length + magnitude +width, data = Tornado3) summary(m_injury2)
## ## Call: ## lm(formula = injured_count ~ length + magnitude + width, data = Tornado3) ## ## Residuals: ## Min 1Q Median 3Q Max ## -77.12 -1.22 1.18 2.11 1423.97 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -2.621147 0.405832 -6.459 1.14e-10 *** ## length 0.605839 0.052622 11.513 < 2e-16 *** ## magnitude 18.084474 1.962674 9.214 < 2e-16 *** ## width 0.001498 0.000464 3.228 0.00125 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 25.97 on 6002 degrees of freedom ## (36 observations deleted due to missingness) ## Multiple R-squared: 0.09701, Adjusted R-squared: 0.09656 ## F-statistic: 214.9 on 3 and 6002 DF, p-value: < 2.2e-16
Adding ‘width’ to our model has raised the adjusted R2 slightly.
Predicted Injury Count = -2.621147+0.605(length)+18.08(magnitude)+0.0015(width)
Diagnostic Plots
Diagnostic Plots
Diagnostic Plots
Log Transformations
lm_log.model = lm(log1p(injured_count) ~ log1p(magnitude)+log1p(length)+log1p(width), data = Tornado3) summary(lm_log.model)
## ## Call: ## lm(formula = log1p(injured_count) ~ log1p(magnitude) + log1p(length) + ## log1p(width), data = Tornado3) ## ## Residuals: ## Min 1Q Median 3Q Max ## -2.0666 -0.1605 -0.0479 0.0330 5.1874 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -0.205797 0.037489 -5.490 4.19e-08 *** ## log1p(magnitude) 2.239611 0.049779 44.991 < 2e-16 *** ## log1p(length) 0.116873 0.009743 11.995 < 2e-16 *** ## log1p(width) 0.029611 0.007664 3.864 0.000113 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.4973 on 6002 degrees of freedom ## (36 observations deleted due to missingness) ## Multiple R-squared: 0.3802, Adjusted R-squared: 0.3799 ## F-statistic: 1227 on 3 and 6002 DF, p-value: < 2.2e-16
Log Transformations
Log Transformations
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Log Transformations
Conclusion
The coefficients indicate that magnitude, length and width of a tornado are significant in understanding the injuries caused by tornadoes. However, the linear model does not satisfy the conditions for multiple regressions since the residuals do not appear to be nearly normal and seem to contain outliers (even after transforming the variables).