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I have a data set which I describe by this nonlinear model: $$Y_i=\theta_1 x+2\theta_3x^2+\frac{\theta_2 x^3}{3+exp(-\theta_4x +x^2)}+\theta_5+\epsilon_i$$

$$\epsilon_i \sim N(0,\sigma^2)$$ $$i=1,..,n$$

I have problems formulating a hypotheses that the model is linear and describing the testing of that hypotheses.

Any pointers, clues?

Math Magic
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  • You should be more precise. What are your parameters? What ist your independent variable? Why should the modell be "in fact linear"? If x is your independent variable, then your model is not linear at all. – MrYouMath Oct 18 '16 at 21:20
  • Your null would be $\theta_2 = \theta_3 = 0$ and $H_a$: at least one of them is nonzero. If there's evidence to reject the null then you can say with the corresponding confidence that the model is not linear. – Lee David Chung Lin Oct 18 '16 at 21:26
  • Sorry about not being precise. I want to suggest a hypotheses that the model is linear and then show that the hypotheses can be rejected. – Math Magic Oct 18 '16 at 21:33

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