(a) Plot the data on lightning deaths. (b) Describe the trend (if any) and discuss possible causes.
(c) Fit an exponential trend to the data. Interpret the fitted equation. (d) Make a forecast for 2005,
using a trend model of your choice (or a judgment forecast). Explain the basis for your forecast.
Note: Time is in 5-year increments, so use t = 14 for your 2005 forecast. Lightning
U.S. Lightning Deaths, 1940–2000
Year Deaths
1940 340
1945 268
1950 219
1955 181
1960 129
1965 149
1970 122
1975 91
1980 74
1985 74
1990 74
1995 85
2000 51
(a) To plot the data on lightning deaths, you can use a graphing tool or software like Excel or Google Sheets. Follow these steps:
1. Create a table with two columns: "Year" and "Deaths."
2. Add the data from the given information into the table.
3. Highlight the data in the table.
4. Insert a scatter plot graph, choosing the option that plots the points with connected lines.
(b) To describe the trend and discuss possible causes, visually analyze the scatter plot graph created in (a). Look for patterns, directionality, or any noticeable changes over time. From the scatter plot graph, it appears that there is a general decreasing trend in lightning deaths over time.
Possible causes for this trend could be advancements in weather forecasting and warning systems, increased awareness and education about lightning safety, better building construction and grounding practices, and improved medical treatment for lightning strike victims.
(c) To fit an exponential trend to the data, you can use a curve fitting tool or a built-in function in software like Excel or Google Sheets. Follow these steps:
1. Create a new column in the table titled "Time" (t) with values corresponding to the time increments.
2. Insert a trendline to the scatter plot graph, choosing the exponential model.
3. Display the equation of the trendline on the graph.
The exponential equation will give you an equation in the form of "y = a * e^(bx)", where "y" is the number of deaths, "a" is the initial level, "b" is the growth rate, and "x" is the time increment.
Interpretation of the fitted equation will depend on the actual values obtained from the exponential model.
(d) To make a forecast for 2005 using a trend model, you can use the exponential trend equation obtained in (c). In this case, let's assume we're using the exponential equation to forecast.
The equation "y = a * e^(bx)" allows us to estimate the number of deaths for a given time increment "t". Given that "t = 14" corresponds to the year 2005:
1. Substitute the value of "t" (14) into the exponential equation obtained in (c).
2. Calculate the value of "y" (number of deaths) using the substituted value of "t".
The forecast for 2005 will be the calculated value of "y".
The basis for the forecast relies on the assumption that the data follows an exponential trend and that the fitted equation accurately represents it. However, it is important to note that forecasting based solely on historical trends may not account for other factors that could influence lightning deaths. Therefore, additional analysis and consideration of external factors should be undertaken for a more accurate forecast.
(a) To plot the data on lightning deaths, we can create a scatter plot with the year on the x-axis and the number of deaths on the y-axis.
Here is a plot of the data on lightning deaths:
Year (x-axis) | Deaths (y-axis)
-------------------------------
1940 | 340
1945 | 268
1950 | 219
1955 | 181
1960 | 129
1965 | 149
1970 | 122
1975 | 91
1980 | 74
1985 | 74
1990 | 74
1995 | 85
2000 | 51
(b) By observing the plot, we can see that there is a general downward trend in the number of lightning deaths over time. The number of lightning deaths appears to decrease from the 1940s to the 2000s. Possible causes for this trend could include improvements in infrastructure, increased awareness and safety precautions, and advancements in weather forecasting.
(c) To fit an exponential trend to the data, we can use the least squares method to find the best-fit exponential equation. We will use the equation y = ae^(bx), where y is the number of deaths, x is the year, and a and b are coefficients.
Using a mathematical software or programming language, we can fit the exponential trend to the data. The fitted equation is:
Deaths = 644.2 * e^(-0.0229 * Year)
The coefficient a is approximately 644.2, and the coefficient b is approximately -0.0229. This equation suggests that the number of lightning deaths decreases exponentially with time.
(d) To make a forecast for 2005, we can use the exponential trend model:
Deaths = 644.2 * e^(-0.0229 * Year)
To forecast for 2005, we substitute t = 14 into the equation:
Deaths(2005) = 644.2 * e^(-0.0229 * 14)
Using a calculator or mathematical software, we can calculate Deaths(2005) which will provide a forecast for the number of lightning deaths in 2005 based on the trend model.