Which of the following is NOT a linear regression model?

A. y = w_0 + w_1 * x

B. y = w_0 + w_1 * (x^2)

C. y = w_0 + w_1 * log(x)

D. y = w_0 * w_1 + log(w_1) * x

closed as off-topic by John, kjetil b halvorsen, Juho Kokkala, Tim, gung - Reinstate Monica Dec 9 '15 at 10:46

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  • 2
    $\begingroup$ please add 'self study' tag. it looks like a homework $\endgroup$ – Learner Dec 9 '15 at 6:46
  • 1
    $\begingroup$ "This question does not show any research effort" certainly applies here... $\endgroup$ – Adrian Dec 9 '15 at 10:26

When we say "linear regression" we mean linearity in parameters, not variables. Therefore, A, B and C are linear (the parameters $w_0$ and $w_1$ enter the equations linearly) while D is not (the parameter $w_1$ enters in logarithm).

See also this Wikipedia article, section "Linear regression".

  • $\begingroup$ If this is a self-study question, I know I should have not answered it directly. However, I saw an existing answer that I believe is wrong, so I thought it may be more important to give an alternative (and hopefully correct) answer right away. $\endgroup$ – Richard Hardy Dec 9 '15 at 8:12
  • $\begingroup$ I agree, d is not a linear regression $\endgroup$ – Repmat Dec 9 '15 at 9:40
  • $\begingroup$ Polynomial regression is a special case of multivariate linear regression, so I must agree. $\endgroup$ – d0rmLife Dec 9 '15 at 14:57
  • $\begingroup$ @d0rmLife, OK, it's good that we reached consensus. $\endgroup$ – Richard Hardy Dec 9 '15 at 15:06

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