Least squares modelling (2013)

Class date(s):	08 February 2013
(PDF)	Course slides
Download video: Link (plays in Google Chrome) [352 M]
Download video: Link (plays in Google Chrome) [347 M]
Download video: Link (plays in Google Chrome) [352 M]
Download video: Link (plays in Google Chrome) [290 M]

Course notes and slides

• Course textbook (print chapter 4)
• Slides for class

Software source code

Take a look at the software tutorial.

Code used in class

Least squares demo

x <- c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5)
y <- c(8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68)
plot(x,y)
model.ls <- lm(y ~ x)
summary(model.ls)

coef(model.ls)
confinf(model.ls)

names(model.ls)
model$resisduals
resid(model.ls)

plot(x, y)
abline(model.ls)

Thermocouple data

V <- c(0.01, 0.12, 0.24, 0.38, 0.51, 0.67, 0.84, 1.01, 1.15, 1.31)
T <- c(273, 293, 313, 333, 353, 373, 393, 413, 433, 453)
plot(V, T)
model <- lm(T ~ V)
summary(model)
coef(model)
confint(model)   # get the coefficient confidence intervals
resid(model)     # model residuals
library(car)
qqPlot(resid(model)) # q-q plot of the residuals to check normality

plot(V, T)
v.new <- seq(0, 1.5, 0.1)
t.pred <- coef(model)[1] + coef(model)[2] * v.new
lines(v.new, t.pred, type="l", col="blue")

# Plot x against the residuals to check for non-linearity
plot(V, resid(model))
abline(h=0)

# Plot the raw data and the regression line in red
plot(V, T)
abline(model, col="red")