Why is polynomial regression considered a kind of linear regression? For example, the hypothesis function is h ( x ; t 0 , t 1 , t 2 ) = t 0 + t 1 x + t 2 x 2 ,and the sample points are ( x 1 , y 1 ) , ( x 2 , y 2 ) , …

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Why is polynomial regression considered a kind of linear regression? For example, the hypothesis function is  h  (  x  ;      t    0    ,      t    1    ,      t    2    )  =      t    0    +      t    1    x  +      t    2        x    2    ,and the sample points are  (      x    1    ,      y    1    )  ,  (      x    2    ,      y    2    )  ,  …

Antonio Dickerson · Accepted Answer

This is a form of linear regression because it takes the form  h  (  x  )  =      ∑    i        t    i        f    i    (  x  )    ,which is a linear combination of functions       f    i    (  x  ) and is amenable to a solution using only linear algebra. The non-linearity of the functions       f    i    (  x  ) doesn&#039;t complicate the solution; it enters only in calculating the values       f    i    (      x    j    ), and everything is then linear in these values. What&#039;s important is that the function is linear in the parameters       t    i  ; otherwise these need to be determined by non-linear optimization.

Why is polynomial regression considered a kind of linear regression? For example, the hypothesis fun

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