Logistic regression was used to relate anthropogenic (man-made) and natural factors to the occurrence of elevated concentrations of nitrite plus nitrate as nitrogen in ground water in the Columbia Basin Ground Water Management Area, eastern Washington. Variables that were analyzed included well depth, depth of well casing, ground-water recharge rates, presence of canals, fertilizer application amounts, soils, surficial geology, and land-use types. The variables that best explain the occurrence of nitrate concentrations above 3 milligrams per liter in wells were the amount of fertilizer applied annually within a 2-kilometer radius of a well and the depth of the well casing; the variables that best explain the occurrence of nitrate above 10 milligrams per liter included the amount of fertilizer applied annually within a 3-kilometer radius of a well, the depth of the well casing, and the mean soil hydrologic group, which is a measure of soil infiltration rate. Based on the relations between these variables and elevated nitrate concentrations, models were developed using logistic regression that predict the probability that ground water will exceed a nitrate concentration of either 3 milligrams per liter or 10 milligrams per liter. Maps were produced that illustrate the predicted probability that ground-water nitrate concentrations will exceed 3 milligrams per liter or 10 milligrams per liter for wells cased to 78 feet below land surface (median casing depth) and the predicted depth to which wells would need to be cased in order to have an 80-percent probability of drawing water with a nitrate concentration below either 3 milligrams per liter or 10 milligrams per liter. Maps showing the predicted probability for the occurrence of elevated nitrate concentrations indicate that the irrigated agricultural regions are most at risk. The predicted depths to which wells need to be cased in order to have an 80-percent chance of obtaining low nitrate ground water exceed 600 feet in the irrigated agricultural regions, whereas wells in dryland agricultural areas generally need a casing in excess of 400 feet. The predicted depth to which wells need to be cased to have at least an 80-percent chance to draw water with a nitrate concentration less than 10 milligrams per liter generally did not exceed 800 feet, with a 200-foot casing depth typical of the majority of the area.