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Introduction to R

Introduction to R. Jiang Du Jan 17th 2008. What is R?. A software package for data analysis and graphical representation Scripting language Flexible and customizable Free… Weaknesses Not particularly efficient in handling large data sets Slow in executing big loops. Where to get R?.

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Introduction to R

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  1. Introduction to R Jiang Du Jan 17th 2008

  2. What is R? • A software package for data analysis and graphical representation • Scripting language • Flexible and customizable • Free… • Weaknesses • Not particularly efficient in handling large data sets • Slow in executing big loops

  3. Where to get R? • http://www.r-project.org/

  4. Basic operations > 1+2*3 [1] 7 > log(10) [1] 2.302585 > 4^2 [1] 16 > sqrt(16) [1] 4 > pi [1] 3.141593

  5. Basic operations > x = pi * 2 > x [1] 6.283185 > floor(x) [1] 6 > ceiling(x) [1] 7

  6. Data type: vector > x = c(1,2,3,5,4) > x [1] 1 2 3 5 4 > y = 1:5 > y [1] 1 2 3 4 5 > x + 2 [1] 3 4 5 7 6 > x+y [1] 2 4 6 9 9 > length(x) [1] 5 > sorted_x = sort(x) > sorted_x [1] 1 2 3 4 5

  7. Data type: vector > x [1] 1 2 3 5 4 > x[3] [1] 3 > x[1:2] [1] 1 2 > x[-3] [1] 1 2 5 4 > x[x > 3] [1] 5 4 > x > 3 [1] FALSE FALSE FALSE TRUE TRUE > which(x > 3) [1] 4 5

  8. Data type: matrix > m = matrix(1:9, nrow = 3, ncol = 3, byrow = TRUE) > m [,1] [,2] [,3] [1,] 1 2 3 [2,] 4 5 6 [3,] 7 8 9 > m[1, 2] [1] 2 > m[1:2, 2:3] [,1] [,2] [1,] 2 3 [2,] 5 6

  9. Data type: matrix > m2 = matrix(c(2,0,0,0,2,0,0,0,2), nrow = 3, byrow = TRUE) > m2 [,1] [,2] [,3] [1,] 2 0 0 [2,] 0 2 0 [3,] 0 0 2 > m * m2 [,1] [,2] [,3] [1,] 2 0 0 [2,] 0 10 0 [3,] 0 0 18 > m %*% m2 [,1] [,2] [,3] [1,] 2 4 6 [2,] 8 10 12 [3,] 14 16 18

  10. Date type: data frame > a = c(1:5) > b = a^2 > df = data.frame(a,b) > df a b 1 1 1 2 2 4 3 3 9 4 4 16 5 5 25 > df$b [1] 1 4 9 16 25 > df[3, 2] [1] 9

  11. Data type: data frame > dim(df) [1] 5 2 > subset(df, a > 2) a b 3 3 9 4 4 16 5 5 25 > subset(df, a > 2 & b < 10) a b 3 3 9

  12. Visualization of data > x = 1:10 > y = x^2 > plot(x, y) > z = c(rep(1, 3), rep(5:6, 10), 1:10) > hist(z)

  13. Visualization of data > x = seq(-10, 10, length= 30) > y = x > f = function(x,y) { r <- sqrt(x^2+y^2); 10 * sin(r)/r } > z = outer(x, y, f) > persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")

  14. Visualization of data

  15. Loops, functions, etc. > x = c(1, 2, 3, 4, 5) > y = x > for (i in 1:length(x)) {y[i] = x[i]^2} > y [1] 1 4 9 16 25 > apply(as.array(x), 1, "^", 2) [1] 1 4 9 16 25 > x^2 [1] 1 4 9 16 25

  16. Loops, functions, etc. > x = 1:5 > f3 = function(x) {return(x^3)} > apply(as.array(x), 1, f3) [1] 1 8 27 64 125 > source("~/test.r") [1] -1 -1 9 16 25

  17. One of the most useful commands ? > ?apply

  18. Practice: on Bordeaux wines • Problem • Bordeaux wine vintage quality and the weather • Bordeaux wines in different vintage years have different qualities (reflected in prices) • The older the better? • Weather is an important factor • Hot, dry summer preferred

  19. Practice: the data WRAIN Winter (Oct.-March) Rain ML DEGREES Average Temperature (Deg Cent.) April-Sept. HRAIN Harvest (August and Sept.) ML TIME_SV Time since Vintage (Years)

  20. Practice: load the data > wine_data = read.table("~/wine.data", header = TRUE, na.strings = ".");

  21. Practice: visualization > plot(wine_data$TIME_SV, wine_data$LPRICE2);

  22. Practice: visualization

  23. Practice: visualization

  24. Practice: visualization avg_price = median(wine_data$LPRICE2, na.rm = TRUE); plot(wine_data$DEGREES, wine_data$HRAIN, type = "n", xlab = "Temperature", ylab = "Harvest rain"); points(wine_data$DEGREES[wine_data$LPRICE2 >= avg_price], wine_data$HRAIN[wine_data$LPRICE2 >= avg_price], pch = 19, col = "blue"); points(wine_data$DEGREES[wine_data$LPRICE2 < avg_price], wine_data$HRAIN[wine_data$LPRICE2 < avg_price], pch = 19, col = "red"); legend(15, 250, c(">= avg price", "< avg price"), pch = 19, col = c("blue", "red"));

  25. Practice: linear regression • Find a set of parameters a, …, e, such that: • LPRICE2 ~ a * WRAIN + b * DEGREES + c * HRAIN + d * TIME_SV + e + error_term • The overall error should be minimized • In this case, the sum/average of squared errors • Sum((prediction - actual_price)^2)

  26. Practice: linear regression > lmfit = lm(LPRICE2 ~ WRAIN + DEGREES + HRAIN + TIME_SV, wine_data); > lmfit … Coefficients: (Intercept) WRAIN DEGREES HRAIN TIME_SV -12.145334 0.001167 0.616392 -0.003861 0.023847 > cat("RMS: ", sqrt(sum(lmfit$residuals^2)/length(lmfit$residuals)), "\n"); RMS: 0.2586167

  27. Practice: linear regression

  28. Practice: linear regression plot(wine_data$VINT, wine_data$LPRICE2, xlab = "Vintage year", ylab = "log2 rel. price”, pch = 19, col = "black"); points(wine_data$VINT[30:38], predict(lmfit, wine_data[30:38,]), pch = 19, col = "red"); legend(1965, -0.2, c("old data", "prediction"), pch = 19, col = c("black", "red"));

  29. Practice: linear regression

  30. Practice: linear regression • Using fewer parameters in the model? • LPRICE2 ~ b * DEGREES + c * HRAIN + d + error_term • lmfit2 = lm(LPRICE2 ~ DEGREES + HRAIN, wine_data); • RMS: 0.349513

  31. Links • Classesv2: http://classesv2.yale.edu/ • Course wiki: http://lab.zoo.cs.yale.edu/cs445-wiki/ • R: http://www.r-project.org/ • Bordeaux wine analysis: http://www.liquidasset.com/orley.htm

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