Refer to the Journal of Data Science (Apr. 2004) comparison of methods for estimating rainfall. Exercises 10.11. Consider the simple linear regression relating rain gauge amount (y) to the artificial neural network rain estimate (x).

a. Test whether y is positively related to x. Use α = .10.

b. Construct a 90% confidence interval for β₁. Practically 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