Accurate measurements of rainfall are critical for many hydrological and meteorological projects. Two standard methods of monitoring

Question:

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.

a. Propose a straight-line model relating rain gauge amount (y) to weather radar rain estimate (x).

b. Fit the model to the data using the method of least squares.

c. Graph the least-squares line on a scattergram of the data. Is there visual evidence of a relationship between the two variables? Is the relationship positive or negative?

d. Interpret the estimates of the y-intercept and slope in the words of the problem.

e. Now consider a model relating rain gauge amount (y) to the artificial neural network rain estimate (x). Repeat parts a–d for this model.