# Statistics for Decision Makers - 14.06 - Regression - Non-linear Regression

Title

14.06 - Regression - Non-linear Regression
Author
Bernard Szlachta (NobleProg Ltd) bs@nobleprog.co.uk
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## Non Linear Regression。

 p <- read.csv("http://training-course-material.com/images/4/4f/Pressure.txt",h=T)
options(show.signif.stars=F)
m1 <- lm(pressure  ~ temperature, data=p)
plot(p)
abline(m1)
summary(m1)

m2 <- lm(pressure  ~ temperature + I(temperature^2), data=p)
lines(p$temperature,predict(m2),col="green") summary(m2) m3 <- lm(pressure ~ temperature + I(temperature^2) + I(temperature^3), data=p) lines(p$temperature,predict(m3),col="blue")
summary(m3)


## Nonlinear Regression model output 。

m1
lm(formula = pressure ~ temperature, data = p)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -74.7835    19.6282  -3.810 0.001400
temperature   0.2016     0.0421   4.788 0.000171

Multiple R-squared:  0.5742,	Adjusted R-squared:  0.5492
p-value: 0.000171

m2
lm(formula = pressure ~ temperature + I(temperature^2), data = p)
Estimate Std. Error t value Pr(>|t|)
(Intercept)       2.272e+02  4.229e+01   5.373 6.22e-05
temperature      -1.214e+00  1.941e-01  -6.255 1.15e-05
I(temperature^2)  1.562e-03  2.129e-04   7.336 1.67e-06

Multiple R-squared:  0.9024,	Adjusted R-squared:  0.8902
p-value: 8.209e-09

m3
lm(formula = pressure ~ temperature + I(temperature^2) + I(temperature^3),data = p)
Estimate Std. Error t value Pr(>|t|)
(Intercept)      -4.758e+02  6.580e+01  -7.232 2.92e-06
temperature       3.804e+00  4.628e-01   8.219 6.16e-07
I(temperature^2) -9.912e-03  1.050e-03  -9.442 1.06e-07
I(temperature^3)  8.440e-06  7.703e-07  10.957 1.48e-08

Multiple R-squared:  0.9892,	Adjusted R-squared:  0.987
p-value: 5.889e-15


## Nonlinear Regression model output 。

• Adjusted R2 is AKA ${\bar {R}}^{2}$ , "R bar squared"
• Adjusted R2 spuriously increases when extra explanatory variables are added to the model