Chapter B.6, Problem 28AYU

Diversity and pH The following data represent the number of fish species living in various Andirondack Lakes and the pH of the lakes. From chemistry, we know pH is a measure of the acidity or basicity of a solution. Solutions with pH less than 7 are said to be acidic. As pH increases, the solution is said to be less acidic.

pH	Species
4.6	0
4.7	0
4.8	0
5	0
5	2
5.2	2
5.2	1
5.25	0
5.3	1
5.35	1
5.5	5
5.7	4
5.75	3
5.8	8
6	3
6.1	4
6.2	9
6.25	9
6.3	2
6.3	4
6.3	9
6.4	5
6.7	6
6.7	8
6.7	8
6.8	10

Data based on “Taking the Sting Out of Acid Rain” by David Malakoff Science 12 November 2010 pp. 910–911

1. (a) Draw a scatter diagram of the data treating pH as the explanatory variable.
2. (b) Determine the linear correlation coefficient between pH and number of fish species.
3. (c) Does a linear relation exist between pH and number of fish species?
4. (d) Find the least-squares regression line treating pH as the explanatory variable.
5. (e) Interpret the slope.
6. (f) Is it reasonable to interpret the intercept? Explain.
7. (g) What proportion of the variability in number of fish species is explained by pH?
8. (h) Is the number of fish species in the lake whose pH is 5.5 above or below average? Explain.
9. (i) In part (g), you found the proportion of variability in number of fish species that is explained by the variability in pH. Can you think of other variables that might also explain the variability in the number of fish species?