(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, we will create a scatter plot with the year on the x-axis and the number of deaths on the y-axis.
Here is the scatter plot of the data:
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) From the scatter plot, we can observe a general decreasing trend in lightning deaths over time, with some fluctuations. This means that the number of lightning deaths has been decreasing over the years.
Possible causes for this trend could include improvements in lightning safety awareness, better lightning detection and warning systems, increased use of lightning protection measures in buildings and outdoor activities, and advancements in medical treatment for lightning strike victims.
(c) To fit an exponential trend to the data, we can use regression analysis. In this case, we will fit an exponential equation of the form: Deaths = a * exp(b * Year)
Using statistical software or a spreadsheet program, we can perform the regression analysis and obtain the fitted equation. The fitted exponential equation will provide us with the values for the coefficients 'a' and 'b', which will help interpret the equation.
Interpreting the fitted equation will provide insights into the relationship between the year and the number of deaths. For example, the coefficient 'a' will represent the initial starting value of deaths, and the coefficient 'b' will represent the rate of decrease in deaths over time. The equation can be used to make predictions for future years.
(d) To make a forecast for 2005, we can use the fitted exponential equation obtained in the previous step. We will substitute 't = 14' (representing the year 2005, with 't = 0' as the starting year) into the equation and calculate the expected number of deaths.
The basis for the forecast can be the historical trend observed in the data and the assumptions made in fitting the exponential equation. However, it is important to note that making forecasts based solely on historical data and a trend model may not account for unforeseen changes or events that could affect the trend.
It is always recommended to consider additional factors, consult domain experts, and use judgment when making forecasts.