A2DataDive workshop speakers Alex Ocampo, Chong Zhang, Sangwon Hyun, Yiqun Hu. A2 Data Dive. Feb. 10- 12, 2012. visit the wiki for more information: http://wiki.datawithoutborders.cc/index.php?title=Project:Current_events:A2_DD

1. Author(s): Alex Ocampo, Chong Zhang, Sangwon Hyun, Yiqun Hu, 2012
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3. Descriptive Statistics
quantitatively describe the main features of a collection of data.
How do salaries What should I
vary across the make of all
company? this???!!!
employee
manager
Staff. Jones
HR

4. Descriptive Statistics in R
Mean > mean(x);
> mean(x,trim=a)
Median > median(x)
Mode > sort(table(x))
Standard deviation > sd(x)
Variance > var(x)
the median absolute > mad(c(x))
deviation
interquartile range > IQR(x)
Range > range(x)

5. Data Dimensions
> length(x)
[1] 1000
-------------------------
> nrow(X) Matrix X
[1] 2030
….
> ncol(X)
[1] 100000
> dim(X)
[1] 2034 100000
….

6. Vectorization in R
Matrix X
> apply( X, MARGIN=1, FUN= mean)
> apply( X, MARGIN=2, FUN= mean)

7. 25 boxplot(X)
• Good for small
20
data sets
• Easy to compar
e groups side b
15
y side
• 1.5*IQR defines
10
outlier
5
0
epiE epiS epiImp epilie epiNeur

8. The Big Six
 Minimum, 1st Q, Median, Mean, 3rd Q, Maximu
m
> summary(X)

9. R tries to understand you
> summary(X)

10. Histograms: > hist(X)
epiE epiS epiImp epilie
80
50
Frequency
Frequency
Frequency
Frequency
20 40
40
40
20
0
0
0
0
0 5 10 20 0 4 8 12 0 2 4 6 8 0 2 4 6
epiE epiS epiImp epilie
epiNeur bfagree bfcon bfext
40
40
Frequency
Frequency
Frequency
Frequency
30
40
20
20
0
0
0
0
0 5 15 80 120 160 60 100 160 0 50 150
epiNeur bfagree bfcon bfext
bfneur bfopen bdi
50
Frequency
Frequency
Frequency
60
20
20
0
0
0
40 80 120 80 120 160 0 10 20 30
bfneur bfopen bdi

11. Correlation
> cor(wt,mpg)
[1] -0.8676594
> plot(x=wt,y=mpg) Scatterplot Example
30
Miles Per Gallon
25
20
15
10
2 3 4 5
Car Weight

12. Scatterplot Matrix
• Iris dataset
• 150 flowers
• 5 variables Goingslo, flickr

13. Scatterplot Matrix
plot > pairs(data)
2.0 3.0 4.0 0.5 1.5 2.5
7.5
Sepal.Length
6.0
4.5
4.0
setosa 3.0
Sepal.Width
versicolor
2.0
virginica
7
5
Petal.Length
3
1
2.5
1.5
Petal.Width
0.5
3.0
2.0
Species
1.0
4.5 5.5 6.5 7.5 1 2 3 4 5 6 7 1.0 2.0 3.0

14. > coplot(lat ~ long | depth)
Given : depth
100 200 300 400 500 600
165 170 175 180 185 165 170 175 180 185
-10
-15
-20
lat
-25
-30
-35
165 170 175 180 185 165 170 175 180 185
long

15. Linear Regression
 Why?
 Prediction of future or unknown observations
 Assessment of relationship between variables
 General description of data structure
 What?

16. Variable Selection
 Why?
 Simplification
 Elimination of multicollinearity and noise
 Time and money saving
 How?
 Testing-based Variable Selection Methods
- Backward, Forward, Stepwise
 Criterion-based Procedures
 What?
 AIC = n ln(RSS/n) + 2(p)

17. Example: U.S. State Fact and Figures
 Life Expectancy
 Population, Income, Illiteracy, Murder, HS Grad, Frost, Area
 Selected R code
 Linear Regression
> g <- lm(Life.Exp ~ Population + Income + Illiteracy + Murder
+ HS.Grad + Frost + Area, data = statedata)
> summary(g) Coefficients: Variance Table
Analysis of
Response: Life.Exp
Estimate Std. Error t value Pr(>|t|)
> anova(g) (Intercept) Df Sum Sq Mean Sq F value
7.094e+01 1.748e+00 40.586 Pr(>F)
< 2e-16 ***
Population 5.180e-05 2.919e-05
Population 1 0.4089 0.4089 0.7372 0.395434 .
1.775 0.0832
 AIC Income
Income 1 11.5946 11.5946 20.9028 4.218e-05 ***
-2.180e-05 2.444e-04 -0.089 0.9293
Illiteracy 3.382e-02 19.4207 35.0116 5.228e-07 ***
Illiteracy 1 19.4207 3.663e-01 0.092 0.9269
> step(g) Murder
Murder -3.011e-01 27.4288 49.4486 1.308e-08 ***
1 27.4288 4.662e-02 -6.459 8.68e-08 ***
HS.Grad
HS.Grad 1 4.0989 4.0989 7.3895 0.009494 **
4.893e-02 2.332e-02 2.098 0.0420 *
Frost
Frost 1 2.0488 2.0488 3.6935 0.061426 . .
-5.735e-03 3.143e-03 -1.825 0.0752
Area
Area 1 0.0011 1.668e-06 -0.044
-7.383e-08 0.0011 0.0020 0.964908
0.9649
AIC = n ln(RSS/n) + 2(p) Residuals 42 23.2971 0.5547

18. Continued: U.S. State Fact and Figures
Start: AIC=-22.18
Life.Exp ~ Population + Income + Illiteracy + Murder + HS.Grad + Frost + Area
Df Sum of Sq RSS AIC
- Area 1 0.0011 23.298 -24.182
- Income 1 0.0044 23.302 -24.175
- Illiteracy 1 0.0047 23.302 -24.174
<none> 23.297 -22.185
- Population 1 1.7472 25.044 -20.569
- Frost 1 1.8466 25.144 -20.371
- HS.Grad 1 2.4413 25.738 -19.202
- Murder 1 23.1411 46.438 10.305
Step: AIC=-24.18
Life.Exp ~ Population + Income + Illiteracy + Murder + HS.Grad + Frost
Df Sum of Sq RSS AIC
- Illiteracy 1 0.0038 23.302 -26.174
- Income 1 0.0059 23.304 -26.170
<none> 23.298 -24.182
- Population 1 1.7599 25.058 -22.541
- Frost 1 2.0488 25.347 -21.968
- HS.Grad 1 2.9804 26.279 -20.163
- Murder 1 26.2721 49.570 11.569

19. Continued: U.S. State Fact and Figures
73
Step: AIC=-28.16
Life.Exp ~ Population + Murder + HS.Grad + Frost
Df Sum of Sq RSS AIC Effect on Response Variable of
<none> 23.308 -28.161 One Unit Change of Predict Variable
- Population 1 2.064 25.372 -25.920
Life Expectancy
- Frost 1 3.122 26.430 -23.877
- HS.Grad 1 5.112 28.420 -20.246
- Murder 1 34.816 58.124 15.528
Coefficients:
0.00005014
(Intercept) Population Murder HS.Grad Frost
0.3001
7.103e+01 5.014e-05 -3.001e-01 4.658e-02 -5.943e-03
0.04658 0.005943
71.03
70
Intercept x1 x4 x5 x6
Predict Variables

20. What is Principal Component Analysis (PCA)?
 Two general approaches of reducing variables :
feature selection and feature extraction
 Feature Selection : “Akaike Information
Criterion”(AIC), BIC or Back-Substitution
 Feature extraction : “Principal Component
Analysis”(PCA) is most widely used
 Create several artificial variables
 Built-in functions in R = Convenient!

21. Actual Pima Data
pregnant glucose diastolic triceps insulin bmi diabetes age test
1 6 148 72 35 0 33.6 0.627 50 1
2 1 85 66 29 0 26.6 0.351 31 0
3 8 183 64 0 0 23.3 0.672 32 1
4 1 89 66 23 94 28.1 0.167 21 0
5 0 137 40 35 168 43.1 2.288 33 1
6 5 116 74 0 0 25.6 0.201 30 0
….
( Imagine a data set with many more (~1000) columns )
(Imagine a Linear Regression: Which variables affect diabetes in what ways?)

22. PCA Example: Pima Indians
 The National Institute of Diabetes and Digestive and Kidney Diseases conducte
d a study on 768 adult female Pima Indians living near Phoenix.
 9 Variables (8 continuous, 1 categorical)
 pregnant: Number of times pregnant
 Glucose : Plasma glucose concentration at 2 hours in an oral glucose tolerance test
 Diastolic : Diastolic blood pressure (mm Hg)
 Triceps : Triceps skin fold thickness (mm)
 Insulin : 2-Hour serum insulin (mu U/ml)
 Bmi : Body mass index (weight in kg/(height in metres squared))
 Diabetes : Diabetes pedigree function
 Age : Age (years)
 Test : diabetes (coded 0 if negative, 1 if positive)
 Next Slide: PCA Implementation

23. What principal components might look like:
 PC1 : 1*Insulin + 0.01*Glucose + ..
 PC2 : 1*Glucose + 0.12*Age + 0.12*DiastolicBP + ..
 PC3 : 0.92 * DiastolicBP + 0.31*Triceps
 Principal components : What are they composed of?
(less important)
 Difference with Linear Regression

24. +
++
-4000 -3000 -2000 -1000 0 +
-Goal: obtain summary
0.10
about data in lower
1000
dimensions + +
+ +
+ +
0.05
++ +++
+++ +
+ + + ++ +
+ + + + ++++ ++ ++ +
++++
++
500
+ ++ ++++++++
+ +
+ + ++ +++ +
+ +++ +++
+
+ + + ++++ +
+ + ++++ +
+ + + + ++++ +++ +
++
+
+ + +++ +
+ ++
-- How many + +++++ +
+++ +++ + +
+ ++ +++ +
+ + + + +++ ++
+ + + ++ + + + + +
+ + ++++++ +++++ +
+ ++ +++ +
dimensions? + ++ + ++
+ + + ++
++ + +
+++ ++++ +
+ + ++++ +++++ +
0.00
insulin
+ triceps +
+ +++
0
PC2 + + + + ++
pregnant
+++ + ++ ++++ +
+ +age +
++
bmi +
+ ++++
+ + +diastolic+
+ ++ + + + + ++ ++ + ++
+
++
+ +
++ +
++ + ++ + +
+ ++ + + +
+ + + ++++++ + +
+
-500
+ + + ++
+ +
+
+
- R code in the next +
+ ++ + + ++ + + ++
+
-0.05
+ + ++ +
+
++ + ++ + + +
++
slide: +++ +
glucose +
+
+
+
+++++ + +
-1000
+ ++ +
++ + +
+
+ ++
++
-0.10
+
++
-1500
+
-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00
PC1

25. Brief : R-Code
> data.pca <- prcomp(data[,-9]); summary(data.pca);
Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6 PC7
Standard deviation 116.002 30.5411 19.7630 14.0777 10.6155 6.76973 2.78575
Proportion of Variance 0.889 0.0616 0.0258 0.0131 0.00744 0.00303 0.00051
Cumulative Proportion 0.889 0.950 0.976 0.9890 0.996 0.999 1.00000
> data.pca
Rotation:
PC1 PC2 PC3 PC4 PC5 PC6 PC7
pregnant 0.002 -0.02 0.02 0.05 2e-01 -0.005 -1e+00
glucose -0.098 -0.97 -0.14 -0.12 -9e-02 0.051 -9e-04
Diastolic -0.016 -0.14 0.92 0.26 -2e-01 0.076 1e-03
triceps -0.061 0.06 0.31 -0.88 3e-01 0.221 4e-04
insulin -0.993 0.09 -0.02 0.07 -2e-04 -0.006 -1e-03
bmi -0.014 -0.05 0.13 -0.19 2e-02 -0.971 3e-03
age 0.004 -0.14 0.13 0.30 9e-01 -0.015 2e-01
> barplot(totalrep, main="Representation of Principal Components", xlab="Principal
Component", ylab="% of Total Variance")
> biplot(data.pca, xlabs=rep('+',768), xlim = c(-0.05,0.3), ylim = c(-0.15,0.12)); abline(h=0,v=0);

26. Representation of Principal Components
0.5
0.4
% of Total Variance
0.3
0.2
0.1
0.0
Principal Component