Arsenic in groundwater. Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit to test for arsenic in groundwater, Exercise 12.16 (p. 725). You fit a first-order model for arsenic level (y) as a function of latitude, longitude, and depth. Based on the model statistics, the researchers concluded that the arsenic level is highest at a low latitude, high longitude, and low depth. Do you agree? If so, find a 95% prediction interval for arsenic level for the lowest latitude, highest longitude, and lowest depth that are within the range of the sample data. Interpret the result.
Exercise 12.16
Arsenic in groundwater. Environmental Science & Technology (January 2005) reported on a study of the reliability of a commercial kit to test for arsenic in groundwater. The field kit was used to test a sample of 328 groundwater wells in Bangladesh. In addition to the arsenic level (micrograms per liter), the latitude (degrees), longitude (degrees), and depth (feet) of each well were measured. The data are saved in the file. (The first and last 5 observations are listed in the table below.)
a. Write a first-order model for arsenic level (y) as a function of latitude, longitude, and depth.
b. Fit the model to the data using the method of least squares.
c. Give practical interpretations of the b estimates.
d. Find the model standard deviation, s, and interpret its value.
e. Find and interpret the values of R2 and R2 a.
f. Conduct a test of overall model utility at a = .05.
g. Based on the results, parts d–f, would you recommend using the model to predict arsenic level (y)? Explain.
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