I am studying the relationship between measured and predicted emission rates for different compounds. Some of the compounds showed linear relationship, while other showed polynomial or power relationship.
Is there any significance to the differences in these equations?
can you please clarify a little more on which is the Dependent variable and which is/are the Independent variable(s) in your postulated regression model ?
The type of trend has implications for the underlying mechanism that regulates the emission. Linear trends have a constant rate of change with one unit change in the x axis inducing the same amount of change in emission no matter where on the axis that occurs. This means linear relationships indicate an additive effect for X. More X adds more emission.
The others suggest the rate changes along the axis, and the nature of the rate change is defined by the type of relation. Polynomials indicate a multiplicative effect for X, more X multiplies the emission. While power trends indicate an exponential effect.
For multiplicative and exponential trends it indicates that X interacts with itself to enhance emission the larger it gets. Note that for polynomial trends it is extremely risky to extrapolate beyond the data (this is generally true of regression, but critical in polynomials).
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