Trace metals in drinking water affect the flavor of the water, and un-usually high concentration can pose a health hazard. Table E8.1 shows trace-metal concentrations (zinc, in mg/L) for both surface water and bottom water at six different river locations. Our aim is to see if surface water concentration (x) is predictive of bottom water concentration ( y).
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TABLE E8.1
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Location
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Bottom
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Surface
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1
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0.430
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0.415
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2
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0.266
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0.238
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3
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0.567
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0.390
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4
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0.531
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0.410
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5
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0.707
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0.605
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6
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0.716
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0.609
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(a) Draw a scatter diagram to show a possible association between the concentrations and check to see if a linear model is justified.
(b) Estimate the regression parameters, the bottom water concentration for location with a surface water concentration of 0.5 mg/L, and draw the regression line on the same graph with the scatter diagram.
(c) Test to see if the two concentrations are independent; state your hypotheses and choice of test size.
(d) Calculate the coefficient of determination and provide your inter- pretation.