A2DataDive workshop: Introduction to R

Author(s): Alex Ocampo, Chong Zhang, Sangwon Hyun, Yiqun Hu, 2012License: Unless otherwise noted, this material is made available under the termsof the Creative Commons Attribution – Noncommercial – Share Alike 3.0 License: http://creativecommons.org/licenses/by-nc-sa/3.0/We have reviewed this material in accordance with U.S. Copyright Law and have tried to maximize your ability to use, share, and adapt it. The citation key on the following slide provides information about how you may share and adapt this material.Copyright holders of content included in this material should contact open.michigan@umich.edu with any questions, corrections, or clarification regarding the use of content.For more information about how to cite these materials visit http://open.umich.edu/education/about/terms-of-use.

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Descriptive Statisticsquantitatively 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

Descriptive Statistics in RMean > 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))deviationinterquartile range > IQR(x)Range > range(x)

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

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

25 boxplot(X) • Good for small20 data sets • Easy to compar e groups side b15 y side • 1.5*IQR defines10 outlier50 epiE epiS epiImp epilie epiNeur

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

R tries to understand you > summary(X)

Histograms: > hist(X) epiE epiS epiImp epilie 80 50Frequency 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 40Frequency 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 50Frequency Frequency Frequency 60 20 20 0 0 0 40 80 120 80 120 160 0 10 20 30 bfneur bfopen bdi

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

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

Scatterplot Matrixplot > 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

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

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

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)

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 0.9649AIC = n ln(RSS/n) + 2(p) Residuals 42 23.2971 0.5547

Continued: U.S. State Fact and FiguresStart: AIC=-22.18Life.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 10.305Step: AIC=-24.18Life.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

Continued: U.S. State Fact and Figures 73Step: AIC=-28.16Life.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 15.528Coefficients: 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

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!

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?)

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

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

+ ++ -4000 -3000 -2000 -1000 0 +-Goal: obtain summary 0.10about data in lower 1000dimensions + + + + + + 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

Brief : R-Code> data.pca <- prcomp(data[,-9]); summary(data.pca);Importance of components: PC1 PC2 PC3 PC4 PC5 PC6 PC7Standard deviation 116.002 30.5411 19.7630 14.0777 10.6155 6.76973 2.78575Proportion of Variance 0.889 0.0616 0.0258 0.0131 0.00744 0.00303 0.00051Cumulative Proportion 0.889 0.950 0.976 0.9890 0.996 0.999 1.00000> data.pcaRotation: PC1 PC2 PC3 PC4 PC5 PC6 PC7pregnant 0.002 -0.02 0.02 0.05 2e-01 -0.005 -1e+00glucose -0.098 -0.97 -0.14 -0.12 -9e-02 0.051 -9e-04Diastolic -0.016 -0.14 0.92 0.26 -2e-01 0.076 1e-03triceps -0.061 0.06 0.31 -0.88 3e-01 0.221 4e-04insulin -0.993 0.09 -0.02 0.07 -2e-04 -0.006 -1e-03bmi -0.014 -0.05 0.13 -0.19 2e-02 -0.971 3e-03age 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);

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

A2DataDive workshop: Introduction to R

by Open.Michigan on Feb 21, 2012

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