Arsenic in groundwater. Environmental Science &

Technology (Jan. 2005) reported on a study of the reliability of a commercial kit designed 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 (in micrograms per liter), the latitude (degrees), longitude (degrees), and depth (feet) of each well were measured. The first and last five observations of the data are listed in the following table.

Wellid Latitude Longitude Depth Arsenic 10 23.7887 90.6522 60 331 14 23.7886 90.6523 45 302 30 23.7880 90.6517 45 193 59 23.7893 90.6525 125 232 85 23.7920 90.6140 150 19 f f f f f 7353 23.7949 90.6515 40 48 7357 23.7955 90.6515 30 172 7890 23.7658 90.6312 60 175 7893 23.7656 90.6315 45 624 7970 23.7644 90.6303 30 254

a. Write a first-order model for arsenic level (y) as a function of latitude, longitude, and depth.

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

c. Give practical interpretations of the b estimates.

d. Find the standard deviation s of the model, and interpret its value.

e. Find and interpret the values of R2 and R2a

.

f. Conduct a test of overall model utility at a = .05.

g. On the basis of the results you obtained in parts d–f, would you recommend using the model to predict arsenic level (y)? Explain.