A conservation scientist records nitrate concentration c c\,c mg L−1^{-1}−1 and a plant-diversity index d d\,d at randomly selected river sites. The correlation coefficient is -0.760, with a one-tailed p-value of 0.006. The regression line fitted for 5≤c≤40 5\leq c\leq40\,5≤c≤40 is d=8.4−0.12cd=8.4-0.12cd=8.4−0.12c.
Test at the 1% significance level whether there is evidence of negative association.
Interpret the gradient of the regression line.
Estimate the diversity index at a site with nitrate concentration 30 mg L−1^{-1}−1.
Explain why the test does not establish that nitrate concentration causes the change in diversity.
Explain why the model should not be used to predict the index when c=70c=70c=70.