Biochemical oxygen demand (BOD) measures organic pollutants in water by measuring the amount of oxygen consumed by microorganisms that break down these compounds. BOD is hard to measure accurately. Total organic carbon (TOC) is easy to measure, so it is common to measure TOC and use regression to predict BOD. A typical regression equation for water entering a municipal treatment plant is BOD = -55.48 + 1.506 TOC Both BOD and TOC are measured in milligrams per liter of water. (a) What does the slope of this line say about the relationship between BOD and TOC? BOD rises (falls) by 1.506 mg/l for every 1 mg/l increase (decrease) in TOCBOD rises (falls) by 55.48 mg/l for every 1 mg/l increase (decrease) in TOC TOC rises (falls) by 1.506 mg/l for every 55.48 mg/l increase (decrease) in BODTOC rises (falls) by 1.506 mg/l for every 1 mg/l increase (decrease) in BOD (b) What is the predicted BOD when TOC = 0? Values of BOD less than 0 are impossible. Why do you think the prediction gives an impossible value? There must be lurking variables; these factors have created a regression equation that allows for impossible values.The regression equation is incorrect; a correct regression equation would never provide impossible values. This arises from extrapolation; the data used to find this regression formula must not have included values of TOC near 0.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Biochemical oxygen demand (BOD) measures organic pollutants in water by measuring the amount of oxygen consumed by microorganisms that break down these compounds. BOD is hard to measure accurately. Total organic carbon (TOC) is easy to measure, so it is common to measure TOC and use regression to predict BOD. A typical regression equation for water entering a municipal treatment plant is

BOD = -55.48 + 1.506 TOC

Both BOD and TOC are measured in milligrams per liter of water.

(a) What does the slope of this line say about the relationship between BOD and TOC?

BOD rises (falls) by 1.506 mg/l for every 1 mg/l increase (decrease) in TOCBOD rises (falls) by 55.48 mg/l for every 1 mg/l increase (decrease) in TOC TOC rises (falls) by 1.506 mg/l for every 55.48 mg/l increase (decrease) in BODTOC rises (falls) by 1.506 mg/l for every 1 mg/l increase (decrease) in BOD

(b) What is the predicted BOD when TOC = 0?
Values of BOD less than 0 are impossible. Why do you think the prediction gives an impossible value?

There must be lurking variables; these factors have created a regression equation that allows for impossible values.The regression equation is incorrect; a correct regression equation would never provide impossible values. This arises from extrapolation; the data used to find this regression formula must not have included values of TOC near 0.

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