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The MathWorks
Data Analysis

Data Analysis

Product catalog summary

Contact Information: The document provides contact details for The MathWorks, including web resources, newsgroups, and email addresses for technical support, product suggestions, bug reports, documentation errors, and sales inquiries. Phone and fax numbers are also included.

License and Copyright: The software is licensed and cannot be copied or reproduced without consent. It is classified as commercial software for federal acquisitions.

Trademarks and Patents: MATLAB and Simulink are registered trademarks, and the products are protected by U.S. patents.

Revision History: The document has undergone several revisions from 2005 to 2008, corresponding to different MATLAB releases.

Data Processing: This section covers importing and exporting data, plotting data, handling missing and inconsistent data, filtering, detrending, differencing, and descriptive statistics. Key tools include the MATLAB Import Wizard and functions for handling NaNs and performing interpolation.

Interactive Data Exploration: Discusses interactive data exploration, including data brushing and linking, which allows for responsive and interactive graph manipulation.

Regression Analysis: Covers linear correlation, covariance, correlation coefficients, linear regression, and fitting data using MATLAB functions and the Curve Fitting Toolbox.

Time Series Analysis: Introduces time series objects and methods, including importing, exporting, plotting, and processing time series data using MATLAB's Time Series Tools.

Inconsistent Data: Outliers are defined as values more than three standard deviations away from the mean. The document provides a MATLAB example to identify and remove outliers from a dataset.

Filtering Data: MATLAB functions can filter data to smooth out high-frequency fluctuations or remove periodic trends. Examples include a moving average filter and a discrete filter.

Detrending Data: The detrend function in MATLAB removes the mean or a best-fit line from data, allowing focus on fluctuations.

Differencing Data: MATLAB offers functions like diff to compute differences between successive elements in a vector.

Descriptive Statistics: MATLAB functions calculate descriptive statistics such as maximum, mean, median, and standard deviation.

Descriptive Statistics and Data Processing in MATLAB: Discusses modifying plot appearance, saving statistics to the workspace, and generating an M-file for reproducing plots and statistics with new data.

Interactive Data Exploration: Involves using tools like data brushing, data linking, and datatips to explore and understand data sets.

Data Brushing: Allows manual selection of observations on interactive displays for further analysis.

Effects of Brushing: Brushing highlights data points without affecting the underlying data.

Brushed 3-D Plots: In 3-D plots, brushing defines a region of interest as a rectangular prism.

Brushed Multiple Plots: Brushing in one plot highlights related observations in linked plots and the Variable Editor.

Marking Up Graphs with Data Brushing: Data brushing in MATLAB allows users to interactively mark data points on graphs.

Making Graphs Responsive with Data Linking: Data linking in MATLAB enables graphs to automatically update in response to changes in workspace variables.

Linking vs. Refreshing Plots: Data linking automates the process of keeping graphs in sync with workspace variables.

Using Linked Plot Controls: The Linked Plot information bar provides controls for managing data links.

Interacting with Graphed Data: Data brushing can be performed in the Variable Editor, where shared variables in linked figures are highlighted.

Overview: The document provides a detailed guide on interacting with graphed data using MATLAB tools, focusing on data exploration techniques such as data brushing, data cursor, and linking plots.

Key Sections:

Interacting with Graphed Data: Discusses the use of the Variable Editor and datatips for exploring data points in graphs.
Using Datatips: Explains how to create and customize datatips using a text update function in M-code.
Example - Exploring Demographic Statistics: Provides a step-by-step example of using datatips to explore traffic accident data across U.S. states.
Plotting and Linking Data: Describes how to plot data, link graphs to their data sources, and use data brushing to highlight and explore relationships between different data sets.
Mapping Observations: Shows how to create a scatter plot of geographic data and link it to other plots for comprehensive data exploration.

Critical Information:

Customization of datatips allows for enhanced data exploration by displaying relevant information such as deviations and labels.
Data linking and brushing are powerful tools for identifying patterns and relationships in data sets.
The example demonstrates practical applications of these techniques in analyzing demographic and socioeconomic data.

Introduction: Before fitting a function to model the relationship between two measured quantities, it is essential to determine if a relationship exists. Correlation quantifies the strength of a linear relationship between two variables.

Covariance: The covariance matrix is symmetrical, with diagonal elements representing variances and off-diagonal elements representing covariances between data columns.

Correlation Coefficients: The correlation coefficient matrix measures the strength of the linear relationship between variables, ranging from -1 to 1.

Linear Regression: Linear regression fits a data model that is linear in the model coefficients, commonly using a least-squares fit.

Residuals and Goodness of Fit: Residuals are the differences between observed and predicted values. A good fit minimizes the sum of the squares of the residuals.

Fitting Data with Curve Fitting Toolbox: The Curve Fitting Toolbox extends MATLAB's capabilities, offering linear and nonlinear parametric fitting, nonparametric fitting, and tools for evaluating the goodness of fit.

Interactive Fitting: The Basic Fitting GUI allows interactive modeling, plotting, and analysis of data fits.

Regression Analysis: Describes how to use MATLAB for regression analysis, specifically focusing on interactive fitting.

Programmatic Fitting: Covers MATLAB functions for polynomial models, including polyfit and polyval.

Linear Models with Nonpolynomial Terms: When polynomial models are insufficient, linear models with nonpolynomial terms can be used.

Multiple Regression: Involves modeling data with more than one predictor variable.

Example: Programmatic Fitting: An example using U.S. census data demonstrates calculating correlation coefficients, fitting a polynomial to data, and plotting confidence bounds.

Time Series Analysis: Involves identifying and modeling patterns in data sampled over time.

Time Series Objects: MATLAB time series objects include timeseries and tscollection.

Example: Time Series Objects and Methods: Provides a step-by-step example of creating and working with time series objects.

Creating Time Series Objects: Explains how to create timeseries objects in MATLAB from a 24-by-3 matrix of traffic data.

Viewing Time Series Objects: Instructions are provided for viewing timeseries objects in MATLAB using the Variable Editor or Time Series Tools.

Modifying Time Series Units and Interpolation Method: Details on changing the units and interpolation method of a timeseries object using dot notation.

Defining Events: Illustrates how to define events in a timeseries object using the tsdata.event object.

Creating Time Series Collection Objects: Instructions for creating a tscollection object to group synchronized time series are given.

Resampling a Time Series Collection Object: Explains how to resample a tscollection object using a new time vector.

Adding a Data Sample to a Time Series Collection Object: Instructions for adding a data sample to a tscollection object are given.

Removing and Interpolating Missing Data: Methods for removing or interpolating missing data in a timeseries are discussed.

Removing a Time Series from a Time Series Collection: Instructions for removing a timeseries from a tscollection object are provided.

Changing a Numerical Time Vector to Date Strings: Describes converting a numerical time vector to MATLAB date strings by setting the StartDate field of the TimeInfo property.

Plotting Time Series Collection Members: Instructions for plotting timeseries collection members are provided.

Time Series Constructor: Additional information on time vector formats and constructor syntax is provided.

Introduction to Time Series Objects: The document provides a comprehensive guide on creating and managing time series objects in MATLAB.

Time Series Constructor Syntax: The document outlines various syntax options for creating timeseries objects.

Time Series Properties: Key properties of timeseries objects are detailed.

Time Series Methods: The document categorizes methods into general methods, data and time manipulation methods, event methods, arithmetic operation methods, and statistical methods.

Time Series Collection Constructor: The document introduces the tscollection object, which groups several timeseries objects with a common time vector.

Conclusion: This technical document serves as a detailed reference for users looking to understand and implement time series analysis in MATLAB.

Overview: This document provides a comprehensive guide on handling time series data using MATLAB, focusing on the Time Series Tools and related methods for data manipulation, analysis, and visualization.

Key Sections:

Time Series Objects: Discusses the properties and methods associated with time series objects.
Time Series Collection Methods: Details methods for querying and setting properties of time series collections.
Time Series Tools: Provides an introduction to the Time Series Tools GUI.
Importing and Exporting Data: Explains the types of data that can be imported into Time Series Tools.

Critical Information:

Data Manipulation: Methods like addts, addsampletocollection, and resample are crucial for modifying time series data.
Importing Data: The Import Wizard facilitates importing data from various sources.
Handling Missing Values: Missing data is replaced with NaNs, which can be removed or interpolated using specific commands in the Time Series Tools.
Exporting Data: Data exported from Time Series Tools may differ in representation from the original imported data.

Recommendations: Utilize the context-sensitive help available in the Time Series Tools for guidance on specific tasks and operations.

Overview: This document provides a comprehensive guide on using Time Series Tools for data analysis, focusing on exporting data, plotting, and customizing plots.

Data Export: Time Series Tools allows users to export analyzed data to a file or the MATLAB workspace.

Plotting Time Series: The document outlines different plot types available in Time Series Tools.

Creating and Customizing Plots: Users can create plots by dragging and dropping data nodes onto Views nodes.

Specific Plot Types:

Time Plots: Useful for identifying outliers, trends, and periodicities by plotting data over time.
Spectral Plots: Used to determine frequencies of periodic variations and apply filters to data.
Histograms: Display data distribution by counting values within specified ranges.
Correlation Plots: Show autocorrelation and cross-correlation between time series.

Filtering and Data Manipulation: The document explains how to apply ideal pass or stop filters using spectral plots.

Conclusion: Time Series Tools offers robust functionalities for analyzing and visualizing time series data.

Cross-Correlation Algorithm: The document describes a cross-correlation algorithm used in Time Series Tools.

XY Plots: An XY plot is used to visualize the relationship between two time series by plotting their data values against each other.

Selecting Data for Analysis: Data can be selected using logical expressions, graphical methods, or by excluding certain data points.

Editing Data, Time, Attributes, and Events: Users can display and edit time series data in a table format.

Processing and Manipulating Time Series: The document outlines various operations available in Time Series Tools.

Example: Time Series Tools: The document provides a step-by-step example of using Time Series Tools.

Overview: This document provides a comprehensive guide on using MATLAB's Time Series Tools for time series analysis.

Specifications: The document specifies how to record M-code, import data into Time Series Tools, and create time series from data arrays.

Procedures:

Recording M-code: Users can record M-code by selecting the appropriate options in the Time Series Tools window.
Importing Data: Data can be imported from the MATLAB workspace using the Import Wizard.
Creating Time Plots: Time series can be dragged into the Time Plots node to create visual representations.
Resampling Time Series: The document explains how to resample time series data.
Exporting Data: Time series can be exported to the MATLAB workspace or other formats.

Norms and Recommendations: The document recommends verifying resampled data by examining the time vector.

Key Data and Visuals: The document includes instructions for creating and interpreting various plots.

Critical Information:

The Record M-Code feature is limited to time series data actions.
Resampling is performed one time series at a time.

Catalog excerpts

TimeSeriesTools 2 Inthe TimeSeriesSession tree,draganddropthe > intersection2 and > intersection3 timeseriesinto View1 toaddthemtotheplot. >

Open the catalog to page 205

TimeSeriesAnalysis 2 Draganddropthe intersection2 timeseriesintothe View2 node.Thiscreatesthefollowing XY plot. >

Open the catalog to page 212

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