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I want to regress a variable $y$ onto $x,x^2,\ldots,x^5$. Should I do this using raw or orthogonal polynomials? I looked at question on the site that deal with these, but I don't really understand what's the difference between using them.

Why can't I just do a "normal" regression to get the coefficients $\beta_i$ of $y=\sum_{i=0}^5 \beta_i x^i$ (along with p-values and all the other nice stuff) and instead have to worry whether using raw or orthogonal polynomials? This choice seems to me to be outside the scope of what I want to do.

In the stat book I'm currently reading (ISLR by Tibshirani et al) these things weren't mentioned. Actually, they were downplayed in a way.
The reason is, AFAIK,that in the lm() function in R, using y ~ poly(x, 2) amounts to using orthogonal polynomials and using y ~ x + I(x^2) amounts to using raw ones. But on pp. 116 the authors say that we use the first option because the latter is "cumbersome" which leaves no indication that these commands actually to completely different things (and have different outputs as a consequence).
(third question) Why would the authors of ISLR confuse their readers like that?

I want to regress a variable $y$ onto $x,x^2,\ldots,x^5$. Should I do this using raw or orthogonal polynomials? I looked at the question on the site that deals with these, but I don't really understand what's the difference between using them.

Why can't I just do a "normal" regression to get the coefficients $\beta_i$ of $y=\sum_{i=0}^5 \beta_i x^i$ (along with p-values and all the other nice stuff) and instead have to worry whether using raw or orthogonal polynomials? This choice seems to me to be outside the scope of what I want to do.

In the stat book I'm currently reading (ISLR by Tibshirani et al) these things weren't mentioned. Actually, they were downplayed in a way.
The reason is, AFAIK, that in the lm() function in R, using y ~ poly(x, 2) amounts to using orthogonal polynomials and using y ~ x + I(x^2) amounts to using raw ones. But on pp. 116 the authors say that we use the first option because the latter is "cumbersome" which leaves no indication that these commands actually do two completely different things (and have different outputs as a consequence).
(third question) Why would the authors of ISLR confuse their readers like that?

I want to regress a variable $y$ onto $x,x^2,\ldots,x^5$. Should I do this using raw or orthogonal polynomials. I looked at question on the site that deal with these, but I don't really understand what's the difference between using them.

Why can't I just do a "normal" regression to get the coefficients $\beta_i$ of $y=\sum_{i=0}^5 \beta_i x^i$ (along with p-values and all the other nice stuff) and instead have to worry whether using raw or orthogonal polynomials? This choice seems to me to be outside the scope of what I want to do.

In the stat book I'm currently reading (ISLR by Tibshirani et al) these things weren't mentioned. Actually, they were downplayed in a way.
The reason is, AFAIK,that in the lm() function in R, using y ~ poly(x, 2) amounts to using orthogonal polynomials and using y ~ x + I(x^2) amounts to using raw ones. But on pp. 116 the authors say that we use the first option because the latter is "cumbersome" which leaves no indication that these commands actually to completely different things (and have different outputs as a consequence).
Why would the authors of ISLR confuse their readers like that?

I want to regress a variable $y$ onto $x,x^2,\ldots,x^5$. Should I do this using raw or orthogonal polynomials? I looked at question on the site that deal with these, but I don't really understand what's the difference between using them.

Why can't I just do a "normal" regression to get the coefficients $\beta_i$ of $y=\sum_{i=0}^5 \beta_i x^i$ (along with p-values and all the other nice stuff) and instead have to worry whether using raw or orthogonal polynomials? This choice seems to me to be outside the scope of what I want to do.

In the stat book I'm currently reading (ISLR by Tibshirani et al) these things weren't mentioned. Actually, they were downplayed in a way.
The reason is, AFAIK,that in the lm() function in R, using y ~ poly(x, 2) amounts to using orthogonal polynomials and using y ~ x + I(x^2) amounts to using raw ones. But on pp. 116 the authors say that we use the first option because the latter is "cumbersome" which leaves no indication that these commands actually to completely different things (and have different outputs as a consequence).
(third question) Why would the authors of ISLR confuse their readers like that?

I want to regress a variable $y$ onto $x,x^2,\ldots,x^5$. Should I do this using raw or orthogonal polynomials. I looked at question on the site that deal with these, but I don't really understand what's the difference between using them.

Why can't I just do a "normal" regression to get the coefficients $\beta_i$ of $y=\sum_{i=0}^5 \beta_i x^i$ (along with p-values and all the other nice stuff) and instead have to worry whether using raw or orthogonal polynomials? This choice seems to me to be outside the scope of what I want to do.

In the stat book I'm currently reading (ISLR by Tibshirani et al) these things weren't mentioned.
(And which R command in lm() should I use, y ~ poly(x, 2) or y ~ x + I(x^2) to get this just done?)

I want to regress a variable $y$ onto $x,x^2,\ldots,x^5$. Should I do this using raw or orthogonal polynomials. I looked at question on the site that deal with these, but I don't really understand what's the difference between using them.

Why can't I just do a "normal" regression to get the coefficients $\beta_i$ of $y=\sum_{i=0}^5 \beta_i x^i$ (along with p-values and all the other nice stuff) and instead have to worry whether using raw or orthogonal polynomials? This choice seems to me to be outside the scope of what I want to do.

In the stat book I'm currently reading (ISLR by Tibshirani et al) these things weren't mentioned. Actually, they were downplayed in a way.
The reason is, AFAIK,that in the lm() function in R, using y ~ poly(x, 2) amounts to using orthogonal polynomials and using y ~ x + I(x^2) amounts to using raw ones. But on pp. 116 the authors say that we use the first option because the latter is "cumbersome" which leaves no indication that these commands actually to completely different things (and have different outputs as a consequence).
Why would the authors of ISLR confuse their readers like that?