Algae-fixed organic matter will be produced in a clear-water sample with zero chemical oxygen demand (COD) and biochemical oxygen demand (BOD) through the addition of controlled amounts of nitrogen. A laboratory study using 15-day specimens and sensibly constant phosphorus yields:
(a) Determine the regression line for COD versus nitrogen. Estimate α, β, and σ.
(b) Test if the slope estimate is significantly different from zero at the 5 percent significance level.
(c) Is the intercept zero? Test the hypothesis at the 5 percent level.
(d) What is a 90 percent upper confidence limit on the variance of COD for any value of nitrogen?
(e) Plot the residuals on normal probability paper. Is the normality assumption reasonable?
(f) Plot the residuals versus the independent variable. Does the data appear to satisfy the condition that σ is constant ? Given a large amount of data, how might you test the hypothesis?