View source for Least squares modelling (2014)

__NOTOC__{{ClassSidebar
| date = 29 January 2014 to 26 February 2014
| dates_alt_text = 
| vimeoID1 = Ja1tJeDPUds
| vimeoID2 = 85489099
| vimeoID3 = pkgwO8q0Oig
| vimeoID4 = qeuQNS-g05w
| vimeoID5 = QuO4R_ynd3M
| vimeoID6 = 4PmKI3lOQXk
| vimeoID7 = AkJcGmmT2S8
| vimeoID8 = pVzMPZYFzGE
| course_notes_PDF = 2014-4C3-6C3-Least-squares-modelling.pdf 
| course_notes_alt = Course slides
| overheads_PDF = 
| assignment_instructions = 
| assignment_solutions = 
| video_download_link_MP4 = http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-04C.mp4
| video_download_link_MP4_size = 119M
| video_notes1 =
| video_download_link2_MP4 =http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-04D.mp4
| video_download_link2_MP4_size = 304 M
| video_notes2 =
| video_download_link3_MP4 = http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05A.mp4
| video_download_link3_MP4_size = 291 M
| video_notes3 =
| video_download_link4_MP4 = http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05B.mp4
| video_download_link4_MP4_size = 216 M
| video_notes4 =
| video_download_link5_MP4 = http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05C.mp4
| video_download_link5_MP4_size = 276 M 
| video_notes5 =
| video_download_link6_MP4 =  http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-06A.mp4
| video_download_link6_MP4_size = 239 M
| video_notes6 =
| video_download_link7_MP4 = http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-06B.mp4
| video_download_link7_MP4_size = 259 M
| video_notes7 =
| video_download_link8_MP4 = http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-07B.mp4
| video_download_link8_MP4_size = 277 M
| video_notes8 =
}}

== Course notes and slides ==

* [http://learnche.mcmaster.ca/pid/?source=Least-squares Course textbook] (print chapter 4)
* [[Image:Nuvola_mimetypes_pdf.png|20px|link=Media:2014-4C3-6C3-Least-squares-modelling.pdf ]] [[Media:2014-4C3-6C3-Least-squares-modelling.pdf |Slides for class]] 

{| class="wikitable"  style="text-align: center;"
|-
! Date
! Class number
! colspan="2"|Video and audio files
! Other materials
! Reading (PID)
! Slides
|-
| 29 January
| 04C
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-04C.mp4 Video] (119 M)  
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-04C.mp3 Audio] (18 M) 
| None
| rowspan="10"|[http://learnche.mcmaster.ca/pid/?source=Least-squares Chapter 4]
| rowspan="10"|[[Image:Nuvola_mimetypes_pdf.png|20px|link=Media:2014-4C3-6C3-Least-squares-modelling.pdf]] [[Media:2014-4C3-6C3-Least-squares-modelling.pdf|Slides for class]] 
|-
| 30 January
| 04D
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-04D.mp4 Video] (304 M)  
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-04D.mp3 Audio] (42 M) 
| See the source code below
|-
| 03 February
| 05A
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05A.mp4 Video] (291 M)  
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05A.mp3 Audio] (41 M) 
| See the source code below
|-
| 05 February
| 05B
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05B.mp4 Video] (216 M)  
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05B.mp3 Audio] (42 M) 
| None
|-
| 06 February
| 05C
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05C.mp4 Video] (276 M) 
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-05C.mp3 Audio] (42 M) 
| [[Media:2014-4C3-6C3-Least-squares-practice-problems.pdf|Practice problems]] (with partial solutions)
|-
| 10 February
| 06A
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-06A.mp4 Video] (239 M) 
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-06A.mp3 Audio] (43 M) 
| None
|-
| 12 February
| 06B
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-06B.mp4 Video] (259 M) 
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-06B.mp3 Audio] (42 M) 
| None
|-
| 13 February
| NA
| None
| None
| [[Written_midterm_-_2014|Collaborative midterm]]
|-
| 24 February
| 07A
| None
| None
| style="text-align: left;" |
* [[Media:Course-evaluation-2014.pdf|Course evaluation]]
* [[Media:Multiple-linear-regression-learning-2014.pdf|Multiple linear regression exercise]]
|-
| 26 February
| 07B
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-07B.mp4 Video] (277 M) 
| [http://learnche.mcmaster.ca/media/2014-4C3-6C3-Class-07B.mp3 Audio] (41 M) 
| None
|}

== Software source code ==

Take a look at [[Software_tutorial|the software tutorial]], particularly steps 16 to 22.

== Code used in class ==

Least squares demo; [http://www.r-fiddle.org/#/fiddle?id=kLmMLXev&version=1 run this code in your web-browser].
<syntaxhighlight lang="sas">
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)
confint(model.ls)

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

plot(x, y)
abline(model.ls)
</syntaxhighlight>

<!--
Thermocouple data
<syntaxhighlight lang="sas">
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")
</syntaxhighlight>

Multiple linear regression (manually and automatically with R)
<syntaxhighlight lang="sas">
# Calculate the model manually
x1.raw <- c(1,3,4,7,9,9)
x2.raw <- c(9,9,6,3,1,2)
y.raw  <- c(3,5,6,8,7,10)
n <- length(x1.raw)

x1 <- x1.raw - mean(x1.raw)
x2 <- x2.raw - mean(x2.raw)
y <- y.raw - mean(y.raw)

X <- cbind(x1, x2)

# Calculate:  b = inv(X'X) X'y
XTX <- t(X) %*% X    # compare this to cov(X)*(n-1)
XTY <- t(X) %*% y
XTX.inv <- solve(XTX)
b <- XTX.inv %*% XTY
b

# Let R calculate the model:
model <- lm(y.raw ~ x1.raw + x2.raw)
summary(model)
</syntaxhighlight>
 -->