The following regression equations relate to concentrations of chlorophyll (a measure of lake quality—higher levels indicate algae and possible eutrophication), phosphate, and nitrogen.

The following regression equations relate to concentrations of chlorophyll (a measure of lake quality—higher levels indicate algae and possible eutrophication), phosphate, and nitrogen. (Based partially on a problem in Manly, B., Statistics for Environmental Science and Management, 2nd ed., CRC Press, p.71)

The specification of the model by the researcher:

(1) CH = b0 + b1(PH) + b2(NT)

The regression output:

(2) CH = -9.386 + 0.333PH + 1.200NT

Output from an additional regression:

(3) CH = -16.244 + 0.313PH + 0.960NT + 0.412(NT)(PH)

Questions (answer each with single short sentence, or even shorter):

(a) Considering the three variables and how they are arranged in Equation (1), what does the researcher believe is the “cause and effect” relationship among the three variables (i.e., what causes what)?

(b) What is different about (2) and (3)?

(c) What is the effect of increasing NT by 1 unit in Equation 2 and keeping PH fixed?

(d) What is the effect of increasing NT by 1 unit in Equation 3 and keeping PH fixed?

 

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