Homework Answers
The recurrence interval is the time after which two event of the same magnitude repeats. The formula is given by (n+1)/m where n is the number of years and m is the rank. The ranks and recurrence intervals for the discharges have been calculated below:
| Year | Gauge Height | Discharge | Rank | Recurrence interval |
| 1985 | 4.93 | 318 | 18 | 1.166666667 |
| 1986 | 6.79 | 687 | 9 | 2.333333333 |
| 1987 | 5.54 | 440 | 13 | 1.615384615 |
| 1988 | 4.98 | 351 | 17 | 1.235294118 |
| 1989 | 5.62 | 476 | 11 | 1.909090909 |
| 1990 | 5.05 | 364 | 15 | 1.4 |
| 1991 | 5.62 | 476 | 11 | 1.909090909 |
| 1992 | 4.55 | 269 | 19 | 1.105263158 |
| 1993 | 7.14 | 835 | 3 | 7 |
| 1994 | 7.02 | 800 | 5 | 4.2 |
| 1995 | 5.55 | 466 | 12 | 1.75 |
| 1996 | 10.05 | 2370 | 1 | 21 |
| 1997 | 6.79 | 748 | 8 | 2.625 |
| 1998 | 6.14 | 599 | 10 | 2.1 |
| 1999 | 7.13 | 832 | 4 | 5.25 |
| 2000 | 5.09 | 363 | 16 | 1.3125 |
| 2001 | 5.36 | 423 | 14 | 1.5 |
| 2002 | 6.98 | 795 | 6 | 3.5 |
| 2003 | 6.89 | 772 | 7 | 3 |
| 2004 | 9.76 | 2110 | 2 | 10.5 |
Now, we use this to plot a graph of discharge vs recurrence interval. Both axes need to be on a logarithmic scale. This graph is shown below:
The equation shown on the graph is the equation of the trendline. To find the discharge of the 100 year flood, we simply need to substitute x=100 in the equation. Thus, the discharge is 11423.69 cfs.
To find the flood height, we need to plot another graph of discharge vs gauge height. This graph is shown below:
In this case, the trendline is exponential. To find the height of the 100 year flood, we need to substitute x=11423.69 (the 100 year discharge) in the equation on the graph.
Thus, the height is 0.5618x(11423.69)0.3751 = 18.69ft.
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B)Find the least squares linear regression equation for production
budget (independent variable) and box office (dependent variable ).
Use the equation to estimate the box office for a movie with a $45
million production budget. Interpret the meaning of the slope and
the y-intercept (be specific using the context provided
here).
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