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Any model can be linear/nonlinear. Linearity can be in parameters or in variables.

In Y=a+ b*x1 + c*x2 + d*x3

the model is linear in both parameters (b,c,d) and variables(x1,x2,x3)

In Y=a+ (b+c)x1 + c*x2 + d*x3

the model is nonlinear in parameters (b,c,d) and linear in variables(x1,x2,x3)

In Y=a+ bx1 + c*x2*x3 + d*x3

the model is linear in parameters (b,c,d) and nonlinear in variables(x1,x2,x3)

In Y=a+ bx1 + c*x2*x3 + exp(b+d)*x3

the model is nonlinear in parameters (b,c,d) and nonlinear in variables(x1,x2,x3)

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