Mathematics

Column-Oriented Data Sets

Univariate statistical data is typically stored in individual vectors. The vectors can be either 1-by-n or n-by-1. For multivariate data, a matrix is the natural representation but there are, in principle, two possibilities for orientation. By MATLAB convention, however, the different variables are put into columns, allowing observations to vary down through the rows. Therefore, a data set consisting of twenty four samples of three variables is stored in a matrix of size 24-by-3.

Vehicle Traffic Sample Data Set

Consider a sample data set comprising vehicle traffic count observations at three locations over a 24-hour period.

Vehicle Traffic Sample Data Set  

Time	Location 1	Location 2	Location 3
01h00	11	11	9
02h00	7	13	11
03h00	14	17	20
04h00	11	13	9
05h00	43	51	69
06h00	38	46	76
07h00	61	132	186
08h00	75	135	180
09h00	38	88	115
10h00	28	36	55
11h00	12	12	14
12h00	18	27	30
13h00	18	19	29
14h00	17	15	18
15h00	19	36	48
16h00	32	47	10
17h00	42	65	92
18h00	57	66	151
19h00	44	55	90
20h00	114	145	257
21h00	35	58	68
22h00	11	12	15
23h00	13	9	15
24h00	10	9	7

Loading and Plotting the Data

The raw data is stored in the file, count.dat.

•     11    11     9
       7    13    11
      14    17    20
      11    13     9
      43    51    69
      38    46    76
      61   132   186
      75   135   180
      38    88   115
      28    36    55
      12    12    14
      18    27    30
      18    19    29
      17    15    18
      19    36    48
      32    47    10
      42    65    92
      57    66   151
      44    55    90
     114   145   257
      35    58    68
      11    12    15
      13     9    15
      10     9     7
  

Use the load command to import the data.

• load count.dat
  

This creates the matrix count in the workspace.

For this example, there are 24 observations of three variables. This is confirmed by

• [n,p] = size(count)
  n = 
      24
  p = 
       3
  

Create a time vector, t, of integers from 1 to n.

• t = 1:n;
  

Now plot the counts versus time and annotate the plot.

• set(0,'defaultaxeslinestyleorder','-|--|-.')
  set(0,'defaultaxescolororder',[0 0 0])
  plot(t,count), legend('Location 1','Location 2','Location 3',2)
  xlabel('Time'), ylabel('Vehicle Count'), grid on
  

The plot shows the vehicle counts at three locations over a 24-hour period.

Data Analysis and Statistics

Basic Data Analysis Functions