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.)

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 β estimates.
d. Find the model standard deviation, s, and interpret its value.
e. Find and interpret the values of R2 and R2a.
f. Conduct a test of overall model utility at α = .05.
g. Based on the results, parts d-f, would you recommend using the model to predict arsenic level (y)? Explain.

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