Mik M.

# Method of least squares

A magazine 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 20 groundwater wells in a country. In addition to the arsenic level (micrograms per liter) the latitude (degrees) longitude (degrees) and depth (feet) of each well was measured

Data table:
Well_ID   Latitude   Longitude   Depth     Arsenic
1             23.7714   90.6221       30          78
2             23.7764   90.6492       60          65
3             23.7832   90.6321      125        192
4             23.7944   90.6386        30          21
5             23.7644   90.6224      100         187
6             23.7916   90.6228      100         187
7             23.7674   90.6225        45         123
8             23.7694   90.6176        90         285
9             23.7732   90.6147        75         182
10           23.7894   90.6482       125         292
11           23.7852   90.6215         75         182
12           23.7856   90.6207         45           76
13           23.7745   90.6496         90           55
14           23.7479   90.6387         60         179
15           23.7734   90.6487         90         185
16           23.7681   90.6463         90         285
17           23.7754   90.6452         90         185
18           23.7881   90.6489        125        192
19           23.7872   90.6218          30          55
20           23.7818   90.6243        125         192

b.Fit the model to the data using the method of least squares. Let x1 be the latitudes, x2 be the longitudes, x3 be the depths

Answer. y= (?) +(?) x1 (?) x2+(?) x3  Roundthe constant term and the coefficients for x1 and x2. Round the coefficient for x3 to the nearest hundredth as needed

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