# Question: Accurate measurements of rainfall are critical for many hydrological and

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 and saved in the RAINFALL file.

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

b. Use the method of least squares to fit the model to the data in the RAINFALL file.

c. Graph the least squares line on a scatterplot 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. Find and interpret the value of s for this regression.

f. Test whether y is linearly related to x. Use α = .01.

g. Construct a 99% confidence interval for β1. Interpret the result practically.

h. Now consider a model relating rain gauge amount (y) to the artificial neural network rain estimate (x). Repeat parts a-g for this model.

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 and saved in the RAINFALL file.

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

b. Use the method of least squares to fit the model to the data in the RAINFALL file.

c. Graph the least squares line on a scatterplot 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. Find and interpret the value of s for this regression.

f. Test whether y is linearly related to x. Use α = .01.

g. Construct a 99% confidence interval for β1. Interpret the result practically.

h. Now consider a model relating rain gauge amount (y) to the artificial neural network rain estimate (x). Repeat parts a-g for this model.

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