Question: Water quality in Philadelphia has been recently analyzed. Trace metals in drinking water affect the flavor of the water, and unusually high concentrations can pose a health hazard. The following table shows trace-metal concentrations (zinc, in mg/liter) for both surface water and bottom water at 10 different Schuylkill river locations. The aim is to see if surface water concentration (x) is predictive of bottom water concentration (y).

Zinc concentration (mg/liter)

Location Bottom Surface

1 0.430 0.415

2 0.266 0.238

3 0.567 0.390

4 0.531 0.410

5 0.707 0.605

6 0.716 0.609

7 0.354 0.321

8 0.497 0.467

9 0.631 0.619

10 0.399 0.314

a. Plot a scatterplot to show a possible association between the concentrations. Check to see if a linear model is justified.

b. Estimate the regression parameters, estimate 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 scatterplot.

c. Based on the data provided in question #5,

I. Test to see if the two concentrations are independent, state your hypotheses and your choice of the test size.

II. Calculate the coefficient of determination and provide a brief interpretation.