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.

Table:

Table:

Well_ID Latitude Longitude Dept Arsenic

1 23.7714 90.6221 30 326

2 23.7764 90.6492 60 326

3 23.7832 90.6321 125 158

3 23.7832 90.6321 125 158

4 23.7944 90.6386 30 223

5 23.7644 90.6224 100 16

6 23.7916 90.6228 100 16

7 23.7674 90.6225 45 201

8 23.7694 90.6176 90 320

9 23.7732 90.6147 75 627

10 23.7894 90.6482 125 216

11 23.7852 90.6215 75 13

12 23.7856 90.6207 45 143

13 23.7745 90.6496 90 169

14 23.7479 90.6387 60 269

15 23.7734 90.6487 90 281

16 23.7681 90.6463 90 326

17 23.7754 90.6452 90 631

18 23.7881 90.6489 125 43

19 23.7872 90.6218 30 189

20 23.7818 90.6243 125 260

5 23.7644 90.6224 100 16

6 23.7916 90.6228 100 16

7 23.7674 90.6225 45 201

8 23.7694 90.6176 90 320

9 23.7732 90.6147 75 627

10 23.7894 90.6482 125 216

11 23.7852 90.6215 75 13

12 23.7856 90.6207 45 143

13 23.7745 90.6496 90 169

14 23.7479 90.6387 60 269

15 23.7734 90.6487 90 281

16 23.7681 90.6463 90 326

17 23.7754 90.6452 90 631

18 23.7881 90.6489 125 43

19 23.7872 90.6218 30 189

20 23.7818 90.6243 125 260

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 Round the constant term and the coefficients for x1 and x2. Round the coefficient for x3 to the nearest hundredth as needed

f.Conduct a test of overall model utility at a=0.01. what are the null and alternative hypothesis?

Answer. H0: b1 =b2=b3=0

Ha: At least one b1 ≠ 0

What is the test statistic?

F=

What is the p-value?

p=

***Please show work up

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

f.Conduct a test of overall model utility at a=0.01. what are the null and alternative hypothesis?

Answer. H0: b1 =b2=b3=0

Ha: At least one b1 ≠ 0

What is the test statistic?

F=

What is the p-value?

p=

***Please show work up

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