Mathematics 47: Lecture 2

Transcription

1 Mathematics 47: Lecture 2 Displaying Data Dan Sloughter Furman University March 7, 2006 Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

2 Entering data into R Example Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

3 Entering data into R Example In an experiment to determine the distance at which a bat can detect an insect, the following bat-to-insect detection distances (in centimeters) were observed: 62, 23, 56, 52, 34, 42, 40, 68, 45, 83. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

4 Entering data into R Example In an experiment to determine the distance at which a bat can detect an insect, the following bat-to-insect detection distances (in centimeters) were observed: 62, 23, 56, 52, 34, 42, 40, 68, 45, 83. Methods to input the data to R: Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

5 Entering data into R Example In an experiment to determine the distance at which a bat can detect an insect, the following bat-to-insect detection distances (in centimeters) were observed: 62, 23, 56, 52, 34, 42, 40, 68, 45, 83. Methods to input the data to R: Create a vector x with the data: > x <- c(62, 23, 56, 52, 34, 42, 40, 68, 45, 83) Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

6 Entering data into R Example In an experiment to determine the distance at which a bat can detect an insect, the following bat-to-insect detection distances (in centimeters) were observed: 62, 23, 56, 52, 34, 42, 40, 68, 45, 83. Methods to input the data to R: Create a vector x with the data: > x <- c(62, 23, 56, 52, 34, 42, 40, 68, 45, 83) Alternatively, read the data from a file, say bat.dat: > x <- scan("bat.dat") Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

7 Entering data into R Example In an experiment to determine the distance at which a bat can detect an insect, the following bat-to-insect detection distances (in centimeters) were observed: 62, 23, 56, 52, 34, 42, 40, 68, 45, 83. Methods to input the data to R: Create a vector x with the data: > x <- c(62, 23, 56, 52, 34, 42, 40, 68, 45, 83) Alternatively, read the data from a file, say bat.dat: > x <- scan("bat.dat") Or input the data directly, > x <- scan(), followed by typing in the data (with spaces between entries and a blank line to end input). Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

8 Entering data into R Example In an experiment to determine the distance at which a bat can detect an insect, the following bat-to-insect detection distances (in centimeters) were observed: 62, 23, 56, 52, 34, 42, 40, 68, 45, 83. Methods to input the data to R: Create a vector x with the data: > x <- c(62, 23, 56, 52, 34, 42, 40, 68, 45, 83) Alternatively, read the data from a file, say bat.dat: > x <- scan("bat.dat") Or input the data directly, > x <- scan(), followed by typing in the data (with spaces between entries and a blank line to end input). Or, using R Commander, select New data set from the Data menu. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

9 Entering data into R Example In an experiment to determine the distance at which a bat can detect an insect, the following bat-to-insect detection distances (in centimeters) were observed: 62, 23, 56, 52, 34, 42, 40, 68, 45, 83. Methods to input the data to R: Create a vector x with the data: > x <- c(62, 23, 56, 52, 34, 42, 40, 68, 45, 83) Alternatively, read the data from a file, say bat.dat: > x <- scan("bat.dat") Or input the data directly, > x <- scan(), followed by typing in the data (with spaces between entries and a blank line to end input). Or, using R Commander, select New data set from the Data menu. Note: if you use R Commander, call the data set Bat and relabel var1 as x. Then use Bat$x, to refer to the data. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

10 Stem-and-leaf plot Definition A stem-and-leaf plot is a list of the data, in numerical order, in two columns, with the right column containing the last digits of the numbers. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

11 Example (cont d) The command > stem(x) creates a stem-and-leaf plot: The decimal point is 1 digit(s) to the right of the Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

12 Example (cont d) The command > stem(x) creates a stem-and-leaf plot: The decimal point is 1 digit(s) to the right of the The command > stem(x, scale=2) will expand the scale by a factor of 2, giving the more useful stem-and-leaf plot: The decimal point is 1 digit(s) to the right of the Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

13 Example (cont d) After loading R Commander, either selecting Stem-and-leaf display (be sure to select the variable in the dialog box) from the Graphics menu, or entering the command stem.leaf(bat$x) will create: 1 2: represents 12 leaf unit: 1 n: (2) Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

14 Histograms Definition A histogram is a bar graph of the frequency distribution of a set of data. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

15 Histograms Definition A histogram is a bar graph of the frequency distribution of a set of data. Example (cont d) Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

16 Histograms Definition A histogram is a bar graph of the frequency distribution of a set of data. Example (cont d) The R command > hist(x) produces a histogram of the bat-to-insect distances using the intervals [20, 30], (30, 40], (40, 50], (50, 60], (60, 70], (70, 80], and (80, 90]. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

17 Histograms Definition A histogram is a bar graph of the frequency distribution of a set of data. Example (cont d) The R command > hist(x) produces a histogram of the bat-to-insect distances using the intervals [20, 30], (30, 40], (40, 50], (50, 60], (60, 70], (70, 80], and (80, 90]. The command > hist(x, right=false) uses the intervals [20, 30), [30, 40), [40, 50), [50, 60), [60, 70), [70, 80), and [80, 90]. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

18 Histograms Definition A histogram is a bar graph of the frequency distribution of a set of data. Example (cont d) The R command > hist(x) produces a histogram of the bat-to-insect distances using the intervals [20, 30], (30, 40], (40, 50], (50, 60], (60, 70], (70, 80], and (80, 90]. The command > hist(x, right=false) uses the intervals [20, 30), [30, 40), [40, 50), [50, 60), [60, 70), [70, 80), and [80, 90]. The command > hist(x, breaks=10) will use 10 (or so) intervals Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

19 Histograms Definition A histogram is a bar graph of the frequency distribution of a set of data. Example (cont d) The R command > hist(x) produces a histogram of the bat-to-insect distances using the intervals [20, 30], (30, 40], (40, 50], (50, 60], (60, 70], (70, 80], and (80, 90]. The command > hist(x, right=false) uses the intervals [20, 30), [30, 40), [40, 50), [50, 60), [60, 70), [70, 80), and [80, 90]. The command > hist(x, breaks=10) will use 10 (or so) intervals The command > hist(x, breaks=c(20, 35, 45, 65, 85)) will use the intervals [20, 35], (35, 45], (45, 65], and (65, 85]. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

20 Histograms Definition A histogram is a bar graph of the frequency distribution of a set of data. Example (cont d) The R command > hist(x) produces a histogram of the bat-to-insect distances using the intervals [20, 30], (30, 40], (40, 50], (50, 60], (60, 70], (70, 80], and (80, 90]. The command > hist(x, right=false) uses the intervals [20, 30), [30, 40), [40, 50), [50, 60), [60, 70), [70, 80), and [80, 90]. The command > hist(x, breaks=10) will use 10 (or so) intervals The command > hist(x, breaks=c(20, 35, 45, 65, 85)) will use the intervals [20, 35], (35, 45], (45, 65], and (65, 85]. Note: when the intervals are not of equal length, the heights of the rectangles are not frequencies; rather the areas of the rectangles are scaled to be equal to the proportion of observations in the interval. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

21 Example (cont d) The command > hist(x, right=false, main="bat-to-insect Detection Distances", xlab="distance in cm") produces the plot: Bat to Insect Detection Distances Frequency Distance in cm Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

22 Scatter plots Definition For bivariate data (x 1, y 1 ), (x 2, y 2 )..., (x n, y n ), a scatter plot, is a plot of the ordered pairs of data. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

23 Scatter plots Definition For bivariate data (x 1, y 1 ), (x 2, y 2 )..., (x n, y n ), a scatter plot, is a plot of the ordered pairs of data. Example An experiment to measure the yield of wheat for seven different levels of nitrogen gave the following observations: Nitrogen/acre (x) Yield (cwt/acre) (y) Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

24 Example (cont d) Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

25 Example (cont d) If the nitrogen levels are in a vector x and the wheat yields are in a vector y, then the command > plot(x, y, main="wheat Yield vs. Nitrogen Levels", xlab="nitrogen per acre", ylab="wheat Yield (cwt/acre)") creates the scatter plot below. Wheat Yield vs. Nitrogen Levels Wheat Yield (cwt/acre) Nitrogen per acre Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

26 Example Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

27 Example The command > plot(x, y, type="l") will plot the points connected by lines. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

28 Example The command > plot(x, y, type="l") will plot the points connected by lines. In R Commander, after creating the data set, select Scatterplot from the Graphics menu to create a scatterplot. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

29 Printing and graphics in R The command > dev.print() will print the current graph to the default printer. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

30 Printing and graphics in R The command > dev.print() will print the current graph to the default printer. In Windows, the command > window() will create a new graphics window. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

31 Printing and graphics in R The command > dev.print() will print the current graph to the default printer. In Windows, the command > window() will create a new graphics window. In Linux, the command > x11() will create a new graphics window. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13

32 Printing and graphics in R The command > dev.print() will print the current graph to the default printer. In Windows, the command > window() will create a new graphics window. In Linux, the command > x11() will create a new graphics window. The command > dev.set(n) will make window n the active plotting window. Dan Sloughter (Furman University) Mathematics 47: Lecture 2 March 7, / 13