Refer to the Journal of Data Science (Apr. 2004) evaluation of methods for estimating rainfall, Exercise 10.11. Find a 99% prediction interval for the rain gauge amount y when the neural network estimate is x = 3 millimeters. Interpret the result.

Data from Exercise 10.11

Accurate measurements of rainfall are critical for many hydrological and meteorological projects. Two standard methods of monitoring rainfall use rain gauges and weather radar. Both, however, can be contaminated by human and environmental interference. In the Journal of Data Science (Apr. 2004). researchers employed artificial neural networks (i.e., computer-based mathematical models) to estimate rainfall at a meteorological station in Montreal. Rainfall estimates were made every 5 minutes over a 70-minute period by each of the three methods. The data (in millimeters) are listed in the table.

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RAINFALL Time Radar Rain Gauge Neural Network 8:00 A.M. 3.6 1.8 8:05 2.0 1.2 1.8 8:10 1.1 1.2 1.4 8:15 1.3 1.3 1.9 8:20 1.8 1.4 1.7 8:25 2.1 1.4 1.5 8:30 3.2 2.0 2.1 8:35 2.7 2.1 1.0 8:40 2.5 2.5 2.6 8:45 3.5 2.9 2.6 8:50 3.9 4.0 4.0 8:55 3.5 4.9 3.4 9:00 A.M. 6.5 6.2 6.2 9:05 7.3 6.6 7.5 9:10 6.4 7.8 7.2