# [R] poly() in lm() leads to wrong coefficients (but correct residuals)

From: Andreas Neumann <Andreas.Neumann_at_em.uni-karlsruhe.de>
Date: Thu 30 Jun 2005 - 02:19:07 EST

I am using poly() in lm() in the following form.

1> DelsDPWOS.lm3 <- lm(DelsPDWOS[,1] ~ poly(DelsPDWOS[,4],3))

2> DelsDPWOS.I.lm3 <- lm(DelsPDWOS[,1] ~ poly(I(DelsPDWOS[,4]),3))

3> DelsDPWOS.2.lm3 <-

lm(DelsPDWOS[,1]~DelsPDWOS[,4]+I(DelsPDWOS[,4]^2)+I(DelsPDWOS[,4]^3))

1 and 2 lead to identical but wrong results. 3 is correct. Surprisingly (to me) the residuals are the same (correct) in all cases although the coefficients of 1 (and 2) are wrong and do not in any way match the stated regression polynomial. (summaries below)

QUESTION:
Is there a correct way to use poly() in lm() since version 3 becomes quite
tedious if used more often especially with higher order polynomials?

I am using R Version 1.9.0 (2004-04-12).

Andreas Neumann

SUMMARIES:
> summary(DelsDPWOS.lm3)

Call:
lm(formula = DelsPDWOS[, 1] ~ poly(DelsPDWOS[, 4], 3))

Residuals:

1 2 3 4 5 6 7 8 -0.11414 0.12756 -0.21060 0.04636 -0.03244 0.16030 0.04290 -0.03944

9
0.01949

Coefficients:

```                         Estimate Std. Error t value Pr(>|t|)
(Intercept)               1.33333    0.04861  27.430 1.21e-06 ***
poly(DelsPDWOS[, 4], 3)1 -1.27464    0.14583  -8.741 0.000325 ***
```
poly(DelsPDWOS[, 4], 3)2 0.27483 0.14583 1.885 0.118175 poly(DelsPDWOS[, 4], 3)3 0.11590 0.14583 0.795 0.462774
```---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

Residual standard error: 0.1458 on 5 degrees of freedom
Multiple R-Squared: 0.9416,	Adjusted R-squared: 0.9065
F-statistic: 26.86 on 3 and 5 DF,  p-value: 0.001645

> summary(DelsDPWOS.2.lm3)

Call:
lm(formula = DelsPDWOS[, 1] ~ DelsPDWOS[, 4] + I(DelsPDWOS[,
4]^2) + I(DelsPDWOS[, 4]^3))

Residuals:
1        2        3        4        5        6        7        8
-0.11414  0.12756 -0.21060  0.04636 -0.03244  0.16030  0.04290 -0.03944
9
0.01949

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)           -1.486      7.242  -0.205    0.846
DelsPDWOS[, 4]         8.640     14.161   0.610    0.568
I(DelsPDWOS[, 4]^2)   -6.526      8.799  -0.742    0.492
I(DelsPDWOS[, 4]^3)    1.375      1.730   0.795    0.463

Residual standard error: 0.1458 on 5 degrees of freedom
Multiple R-Squared: 0.9416,	Adjusted R-squared: 0.9065
F-statistic: 26.86 on 3 and 5 DF,  p-value: 0.001645

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