Biology and Environmental Science
The water quality in many lakes and rivers is routinely monitored by tracking the turbidity, a measure of the total amount of suspended solids in the water. High turbidity measured in nephelometric turbidity units, or NTUs, suggests murky water. Heavy rains tend to raise river levels and increase turbidity. A sample of weekly rainfall total (x, measured in inches) and turbidity (y, in NTUs) was obtained for the Wide Waters site at Owasco Lake in New York. The data are given in the following table.
a. Find the estimated regression line.
b. Conduct a test of H0: β1 = 0 versus Ha: β1 ≠ 0 with a significance level of 0.05
c. Find an estimate of the expected turbidity if 0.55 inch of rain has fallen within the past week.
d. What proportion of the observed variation in turbidity is explained by this regression model? How do you think this model could be improved?