This dataset contains the number of deaths due to injuries sustained while playing football in the United States over a 24 year period.
The objective of this activity is to develop a model that can be used to predict the number of deaths in future years.
The data were presented in Sports Illustrated, April 29, 1991, page 16. The data were originally reported by the National Center for Catastrophic Sports Injury Research (www.unc.edu/depts/nccsi/).
| Year | Deaths |
| 1967 | 24 |
| 1968 | 36 |
| 1969 | 23 |
| 1970 | 29 |
| 1971 | 20 |
| 1972 | 22 |
| 1973 | 9 |
| 1974 | 11 |
| 1975 | 15 |
| 1976 | 18 |
| 1977 | 10 |
| 1978 | 9 |
| 1979 | 4 |
| 1980 | 9 |
| 1981 | 9 |
| 1982 | 9 |
| 1983 | 4 |
| 1984 | 6 |
| 1985 | 7 |
| 1986 | 11 |
| 1987 | 4 |
| 1988 | 7 |
| 1989 | 4 |
| 1990 | 0 |
There are two variables in this problem; one is the number of Deaths due to football related injuries and the other is Year. Which should be the response (or dependent) variable? Which should be the explanatory (or independent or predictor) variable? Give reasons for your answer.
Construct a scatterplot for the data. Put the response (dependent) variable on the y-axis and the explanatory (independent) variable on the x-axis.
Fit a least squares regression line to the data. Carefully draw the line on the scatterplot.
Calculate the predictions and residuals for all of the points in the regression dataset.
Construct another scatterplot of the residuals on the y-axis and against the predicted values on the x-axis. Comment on any patterns or unusual features of the residual plot.
Think of a way to change your model or transform your data so that the model will be more appropriate for the data. Do your best to calculate the new prediction model and evaluate how well it fits.
Use your final regression model to predict the number of deaths due to football-related injuries in 1991. Do the same for 1992.
According to your regression model, how many football-related deaths does the model predict for 2000, 2001, and 2002? Do you think that these are reasonable predictions? Why or why not?
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