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- Linear Model vs Nonlinear Models

Hello,

Models can be linear and nonlinear and I just learned that a "linear model" is not just a model where the dependent variable ##Y## is connected to independent variables ##X## raised to the 1st power... The model is called "linear" because the coefficients/parameters are not raised to the a power higher than 1. Is that correct?

So a cubic polynomial is also an example of a linear model even if the fitting curve is not a plane or straight line...

On the other hand, a nonlinear model is a function connecting ##Y## and the ##X## via parameters raised to powers higher than 1? For example, would $$Y= a log(X)$$ be still a linear model since the unknown coefficient ##a## is raised to the 1st power? How about $$Y= \frac {a X_1{^2}} {b X_2 ^3}$$ Is it linear or nonlinear since the coefficients ##a## and ##b## are not raised to exponents higher than 1?

Thank you and happy thanksgiving.

Models can be linear and nonlinear and I just learned that a "linear model" is not just a model where the dependent variable ##Y## is connected to independent variables ##X## raised to the 1st power... The model is called "linear" because the coefficients/parameters are not raised to the a power higher than 1. Is that correct?

So a cubic polynomial is also an example of a linear model even if the fitting curve is not a plane or straight line...

On the other hand, a nonlinear model is a function connecting ##Y## and the ##X## via parameters raised to powers higher than 1? For example, would $$Y= a log(X)$$ be still a linear model since the unknown coefficient ##a## is raised to the 1st power? How about $$Y= \frac {a X_1{^2}} {b X_2 ^3}$$ Is it linear or nonlinear since the coefficients ##a## and ##b## are not raised to exponents higher than 1?

Thank you and happy thanksgiving.