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. Recall that you fit a first-order model for arsenic level (y) as a function of latitude (x1), longitude (x2), and depth (x3).
a. Write a model for arsenic level (v) that includes first-order terms for latitude, longitude, and depth, as well as terms for interaction between latitude and depth and interaction between longitude and depth.
b. Use statistical software to fit the interaction model, part a, to the data. Give the least squares prediction equation.
c. Conduct a test (at α = .05) to determine whether latitude and depth interact to affect arsenic level.
d. Conduct a test (at α = .05) to determine whether longitude and depth interact to affect arsenic level.
e. Practically interpret the results of the tests, parts c and d.
Exercise 12.16
Environmental Science & Technology (Jan. 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.)

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Well ID Latitude Longitude Depth Arsenic 10 23.7887 90.6522 14 23.7886 90.6523 30 23.7880 90.6517 59 23.7893 90.6525 85 23.7920 90.6140 60 45 45 125 150 331 302 193 232 19 7353 23.7949 90.6515 735723.7955 90.6515 7890 23,7658 90.6312 7893 23.7656 90.6315 7970 23.7644 90.6303 30 60 45 30 48 172 175 624 254