Question

Question: Chemical plant contamination. Refer to Exercise 12.18 (p. 725) and the U.S. Army Corps of Engineers study. You fit the first-order model,$\mathbf{E}\mathbf{\left(}\mathbf{Y}\mathbf{\right)}\mathbf{=}{\mathbf{\beta }}_{\mathbf{0}}\mathbf{+}{\mathbf{\beta }}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{\beta }}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{\beta }}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{3}}$ , to the data, where y = DDT level (parts per million),${\mathit{X}}_{\mathbf{1}}$= number of miles upstream,${\mathit{X}}_{\mathbf{2}}$= length (centimeters), and${\mathit{X}}_{\mathbf{3}}$= weight (grams). Use the Excel/XLSTAT printout below to predict, with 90% confidence, the DDT level of a fish caught 300 miles upstream with a length of 40 centimeters and a weight of 1,000 grams. Interpret the result.

Short answer

With 90% accuracy, it can be concluded that the mean DDT level of fish will be between the interval (3.8650, 33.8956)

Step-by-step solution

Step-by-Step SolutionStep 1: Confidence interval interpretation

The 90% confidence interval for DDT level of fish caught 300 miles upstream with a length of 40 cm and weight of 1000 grams is given in the image as (3.8650, 33.8956). This means that with 90% accuracy, it can be concluded that the mean DDT level of fish will be between the interval (3.8650, 33.8956)

Predicted value interpretation

The predicted value of the DDT level of fish calculated here is also 18.8803 which lies within the interval indicating that the predicted value is close to the actual value with 90% accuracy.