I need to export a final multivariate polynomial regression equation from R to another application. I do not understand one portion of the regression output. The regression uses the polym() function. The summary table is posted below.
ploy_lm <- lm(df$SV ~ polym(df$Indy, df$HI, degree = 3, raw = TRUE)
summary(ploy_lm)
The table below says polym input for "df$Indy, df$HI, degree = 3, raw = TRUE".
Estimate | |
---|---|
Intercept | -8.903 |
(polym input)1.o | 1.189E0 |
(polym input)2.o | -1.651E-2 |
(polym input)1.1 | 8.247E-4 |
How do I translate the results into a final regression equation? Does the value at the end of the first column (e.g. from the last row: "polym(df$Indy, df$WM_HI, degree = 3, raw = TRUE)1.1") signify the exponent value?
Here is a simple example with a predefined function:
x1<- runif(20, 1, 20)
x2 <- runif(20, 15, 30)
#define a function for y
y <- (1 - 3*x1 + 1/5*x2 - x1*x2 + 0.013*x1^2 + 0.2 *x2^2)
#add some noise to prevent a warning on the fit
y <- y +rnorm(20, 0, 0.01)
ploy_lm <- lm(y ~ polym(x1, x2, degree = 2, raw = TRUE))
summary(ploy_lm)
Call:
lm(formula = y ~ polym(x1, x2, degree = 2, raw = TRUE))
Residuals:
Min 1Q Median 3Q Max
-0.017981 -0.007537 0.001757 0.005833 0.018697
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.588e-01 7.158e-02 13.39 2.25e-09 ***
polym(x1, x2, degree = 2, raw = TRUE)1.0 -3.003e+00 2.820e-03 -1064.88 < 2e-16 ***
polym(x1, x2, degree = 2, raw = TRUE)2.0 1.315e-02 9.659e-05 136.15 < 2e-16 ***
polym(x1, x2, degree = 2, raw = TRUE)0.1 2.059e-01 6.536e-03 31.51 2.12e-14 ***
polym(x1, x2, degree = 2, raw = TRUE)1.1 -1.000e+00 1.059e-04 -9446.87 < 2e-16 ***
polym(x1, x2, degree = 2, raw = TRUE)0.2 1.998e-01 1.511e-04 1322.68 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.01167 on 14 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 1
F-statistic: 6.298e+08 on 5 and 14 DF, p-value: < 2.2e-16
#In summary
# Term model Fitted
# Intercept 1 .959
# x1 -3 -3
# x1^2 0.013 .0132
# x2 0.2 .206
# x2^2 0.2 .1998
# x1 * x2 -1 -1
The first digit after the ")" is the power of the first term and the number after the "." is the power of the second term.