The document provides an overview of classical decomposition for time series analysis. It explains that classical decomposition can be used to isolate the trend, seasonal, and cyclical components of a time series. The document then describes the basic steps of classical decomposition, which include determining seasonal indexes, deseasonalizing the data, developing a trend-cyclical regression equation, and creating a forecast using trend data and seasonal indexes. An example applying these steps to sales data for a company is also presented.
Unit I (8 Hrs)
Introduction to Linear Programming – Various definitions, Statements of basic
theorems and properties, Advantages Limitations and Application areas of Linear
Programming, Linear Programming -Graphical method, - graphical solution
methods of Linear Programming problems, The Simplex Method: -the Simplex
Algorithm, Phase II in simplex method, Primal and Dual Simplex Method, Big-M
Method
Unit II (8 Hrs)
Transportation Model and its variants: Definition of the Transportation Model
-Nontraditional Transportation Models-the Transportation Algorithm-the Assignment
Model– The Transshipment Model
Unit III (8 Hrs)
Network Models: Basic differences between CPM and PERT, Arrow Networks,
Time estimates, earliest completion time, Latest allowable occurrences time,
Forward Press Computation, Backward Press Computation, Representation in
tabular form, Critical Path, Probability of meeting the scheduled date of completion,
Various floats for activities, Critical Path updating projects, Operation time cost trade
off Curve project,
Selection of schedule based on :- Cost analysis, Crashing the network
Sequential model & related problems, processing n jobs through – 1 machine & 2
machines
Unit IV (8 Hrs)
Network Models: Scope of Network Applications – Network definitions, Goal
Programming Algorithms, Minimum Spanning Tree Algorithm, Shortest Route
Problem, Maximal flow model, Minimum cost capacitated flow problem
Unit V (8 Hrs)
Decision Analysis: Decision - Making under certainty - Decision - Making under
Risk, Decision
under uncertainty.
Unit VI (8 Hrs)
Simulation Modeling: Monte Carlo Simulation, Generation of Random Numbers,
Method for
Gathering Statistical observations
Unit I (8 Hrs)
Introduction to Linear Programming – Various definitions, Statements of basic
theorems and properties, Advantages Limitations and Application areas of Linear
Programming, Linear Programming -Graphical method, - graphical solution
methods of Linear Programming problems, The Simplex Method: -the Simplex
Algorithm, Phase II in simplex method, Primal and Dual Simplex Method, Big-M
Method
Unit II (8 Hrs)
Transportation Model and its variants: Definition of the Transportation Model
-Nontraditional Transportation Models-the Transportation Algorithm-the Assignment
Model– The Transshipment Model
Unit III (8 Hrs)
Network Models: Basic differences between CPM and PERT, Arrow Networks,
Time estimates, earliest completion time, Latest allowable occurrences time,
Forward Press Computation, Backward Press Computation, Representation in
tabular form, Critical Path, Probability of meeting the scheduled date of completion,
Various floats for activities, Critical Path updating projects, Operation time cost trade
off Curve project,
Selection of schedule based on :- Cost analysis, Crashing the network
Sequential model & related problems, processing n jobs through – 1 machine & 2
machines
Unit IV (8 Hrs)
Network Models: Scope of Network Applications – Network definitions, Goal
Programming Algorithms, Minimum Spanning Tree Algorithm, Shortest Route
Problem, Maximal flow model, Minimum cost capacitated flow problem
Unit V (8 Hrs)
Decision Analysis: Decision - Making under certainty - Decision - Making under
Risk, Decision
under uncertainty.
Unit VI (8 Hrs)
Simulation Modeling: Monte Carlo Simulation, Generation of Random Numbers,
Method for
Gathering Statistical observations
Chapter 7 Forecasting Time Series ModelsLan WangCSU East .docxchristinemaritza
Chapter 7: Forecasting
Time Series Models
Lan Wang
CSU East Bay
Some Time Series Terms
Stationary Data - a time series variable exhibiting no significant upward or downward trend over time.
Moving average
Exponential smoothing
Some Time Series Terms
Nonstationary Data - a time series variable exhibiting a significant upward or downward trend over time.
Regression analysis
Some Time Series Terms
Seasonal Data - a time series variable exhibiting a repeating patterns at regular intervals over time.
Seasonal index
Simple Moving Average
Average random fluctuations in a time series to infer short-term changes in direction
Assumption: future observations will be similar to recent past
Moving average for next period = average of most recent k observations
Moving Average Example
The monthly sales for Telco Batteries, Inc. were as follows:MONTHSALESFebruary21March15April14May13June16July18August20
a. Calculate a 3 month moving average forecast for September
b. Calculate a 2 month moving average forecast for September
c. Which moving average forecast is more accurate?
Moving Average Example
Error Metrics and Forecast Accuracy
Mean absolute deviation (MAD)
Mean square error (MSE)
Mean absolute percentage error (MAPE)
The quality of a forecast depends on how accurate it is in predicting future values of a time series.
8
Telco Batteries Example - continued
Exponential Smoothing
Exponential smoothing model:
Ft+1 = (1 – a )Ft + aAt
= Ft + a (At – Ft )
Ft+1 is the forecast for time period t+1,
Ft is the forecast for period t,
At is the observed value in period t, and
a is a constant between 0 and 1, called the smoothing constant.
Highly effective approach.
10
Exponential Smoothing
The monthly sales for Telco Batteries, Inc. were as follows:MONTHSALESFebruary21March15April14May13June16July18August20
a. Calculate an Exponential Smoothing forecast with alpha = 0.2, for September
b. Calculate an Exponential Smoothing forecast with alpha = 0.3, for September
c. Which Exponential Smoothing forecast is more accurate?
Exponential Smoothing Example - ContinuedalphaMonthSales0.20.3AD(0.2)AD(0.3)SE(0.2)SE(0.3)APE(0.2)APE(0.3)February212121March1521216.006.0036.0036.000.400.40April1419.8019.205.805.2033.6427.040.410.37May1318.6417.645.644.6431.8121.530.430.36June1617.5116.251.510.252.290.060.090.02July1817.2116.170.791.830.623.340.040.10August2017.3716.722.633.286.9310.750.130.16September17.8917.71MAD3.733.53MSE18.5516.45MAPE0.250.23
AD - Absolute Deviation SE Squared error
APE - Absolute Percentage Error
Practice
Attendance in each time period. Please forecast the attendance using exponential smoothing (alpha=0.4 and 0.6).
Use MAD, MSE as guidance, find the better alpha setting for each forecasting model.
Trend Models
Trend is the long-term sweep or general direction of movement in a time series.
We’ll now consider some nonstationary time series techniques that are appropriate for dat ...
Meteorology Lab Report
Introduction
Meteorologists draw conclusions based on all known weather data. Since weather data is
constantly changing, their forecast can change from day to day or from hour to hour. Now, it is
your turn to predict the weather. In this lab activity, you will analyze data collected from a
weather station to create a weather forecast.
Problem:
How can we use the relationships among weather data to produce a forecast?
Hypothesis/Prediction:
Based on the weather data in Table 1 below, make a prediction about the weather from the
data by completing the sentences below.. Make sure your prediction is made before you
create graphs of your weather data.
1. If temperature _____________ increases/decreases, then the dew point will
_____________increase/decrease.
2. If temperature ______________ increases/decreases, then air pressure will
_____________ increase/decrease.
Variables:
For this investigation:
List the independent variable(s):
List the dependent variable(s):
List the controlled variable(s):
Materials:
● Weather data in Table 1
● Weather Maps Symbols Key (see lesson)
● Graphing software or application
● Graphing tutorial (optional)
https://www.wpc.ncep.noaa.gov/html/stationplot_printer.html
https://cdn.flvs.net/cdn/lo/graphing/
Procedures:
1. Using the Weather Data from Table 1, construct a line graph using Time on the X axis
and Temperature for the Y axis. Make sure to plot both the temperature and dew point
on your graph. Be sure to include units and add titles to the graphs. Refer to the graph
example and graphing tutorial in the lesson if needed.
2. Using the Weather Data from Table 1, construct a second line graph using Time on the
X axis and Air Pressure for the Y axis. Be sure to include units and add titles to the
graphs.
3. Select two different times (one day and one night) from Table 1 and create a weather
station model for each. Use the example diagram in the data sections and the Weather
Map Symbol Key in the lesson to guide your weather station models.
4. Complete the Questions and Conclusion section of the lab report.
Graph 1
1. You may plot the data by hand on the template below or follow the steps below to
create your graph.
2. Double click on the graph, then select the tab labeled “sheet 1”.
3. Input the data from Table 1 in the corresponding columns on the spreadsheet.
4. Once you have input all corresponding data, select the tab labeled “Chart” at the
bottom of the table to display your line graphs.
Graph 2
1. You may plot the data by hand on the template below or follow the steps below to
create your graph.
2. Double click on the graph, then select the tab labeled “sheet 1”.
3. Input the data from Table 1 in the corresponding columns on the spreadsheet.
4. Once you have input all corresponding data, select the tab labeled “Chart” at the
bottom of the table to display your line graphs.
Data and Observations:
Table 1: Weather Data from Station 1, Cape Canaveral, Flor ...
Data Science - Part X - Time Series ForecastingDerek Kane
This lecture provides an overview of Time Series forecasting techniques and the process of creating effective forecasts. We will go through some of the popular statistical methods including time series decomposition, exponential smoothing, Holt-Winters, ARIMA, and GLM Models. These topics will be discussed in detail and we will go through the calibration and diagnostics effective time series models on a number of diverse datasets.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
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👨🏫 Andras Palfi, Senior Product Manager, UiPath
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Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
DevOps and Testing slides at DASA ConnectKari Kakkonen
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Generating a custom Ruby SDK for your web service or Rails API using Smithyg2nightmarescribd
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Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
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Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
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The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
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Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
The following presentation is meant to familiarize individuals with classical decomposition. It does not contain an entirely comprehensive study of this statistical tool; however, it should make individuals aware of the benefits that classical decomposition can provide. Individuals who will benefit the most from this learning tool will have a basic background in introductory business statistics and knowledge of simple linear regression. Sources that are used throughout this presentation are cited in the notes below each slide and in the bibliography and readings list. Please contact the creator of this presentation with any questions or comments: Kurt Folke E-mail: kfolke75@hotmail.com Boise State University College of Business & Economics
Also included in this presentation are solutions to the exercise. These solutions are available in hidden slide form in Appendix B.
Definitions taken from … StatSoft Inc. (2003). Time Series Analysis. Retrieved April 21, 2003, from http://www.statsoft.com/textbook/sttimser.html Time series models are functions that relate time to previous values of the model. Accordingly, these models presume what has happened in the past will reoccur in the future. Further examples of possible time series data include earnings, market share, and cash flows.
The multiplicative model Y = TCSe is the product of the trend, cyclical, seasonal, and error (or random) components at some time t . Likewise, the additive model Y = T+C+S+e is the sum of trend, cyclical, seasonal, and error (or random) components at some time t. The trend component is the gradual upward or downward movement found in a time series as a result of many possible factors (such as demand). Cyclical influences are recurrent up or down movements that last for long periods of time (longer than a year). Examples of events that might trigger a cyclical influence include recessions or booms. The seasonal component is an upward and downward movement that is repeated periodically as a result of holidays, seasons, etc. These seasonal influences may be observed as being weekly, monthly, quarterly, yearly, or some other periodic term. The error or random component of a time series is the usually small, erratic movement that does not follow a pattern and can be the result of the weather, strikes, and other unpredictable events.
Definitions taken from … Shim, Jae K. Strategic Business Forecasting. New York: St Lucie, 2000. 269. Classical decomposition is a powerful tool for decomposing the elements of a time series model and studying each component’s sub-patterns. By analyzing each component, management can make educated decisions concerning trend and demand for future periods.
A possible example is … classical decomposition can help a company learn when it is experiencing an abnormally high/low demand for its products.
Steps summarized from … DeLurgio, Stephen, and Bhame, Carl. Forecasting Systems for Operations Management . Homewood: Business One Irwin, 1991. 297-298. The basic steps outlined above encompass the major tasks in classical decomposition. Many sub-steps of these general tasks are shown in the explanation and illustration that follows.
Although both multiplicative and additive time series models can be used in classical decomposition, this presentation will only include the multiplicative model as it is most commonly used. Methods for choosing between using the additive or multiplicative model can be found in … DeLurgio, Stephen, and Bhame, Carl. Forecasting Systems for Operations Management . Homewood: Business One Irwin, 1991. 289-290.
The classical decomposition demonstrated here models trend and cyclical effects together for simplicity and lack of a simple modeling technique for cyclical influences. Note: This assumption is appropriate for short-term forecasts, but forecasts for periods longer than one year should include an adjustment for cyclical influences. Just as the four-quarter moving average is used when dealing with quarterly data, likewise the 12-month moving average should be used when working with monthly data. Regardless of the periodic term used in the moving average, the outcome is the same: the seasonal influences are averaged, and therefore are neither seasonally high, nor seasonally low. Note: The hyperlinks provided in these slides will navigate the operator between the classical decomposition explanation and the classical decomposition illustration . This provides the learner with a conceptual explanation followed by actual application of the process.
Since the simple moving average is centered at the end of one period and the beginning of the next, computing the centered moving average is necessary to ensure that the average is centered at the middle of the period. Through this process, the centered moving average is created to contain no seasonality, and therefore is the trend-cyclical component of the model.
Using the identity Se = (Y/TC) , the seasonal-error component is derived by dividing the original data ( Y ) by the trend-cyclical data ( TC ). The trend-cyclical data is the centered moving average that was developed earlier.
By taking the seasonal-error components and averaging them across the available periods, the unadjusted seasonal index is computed. This computation is demonstrated on slide 22. The adjusting factor is created by dividing the number of periods per year (four since the data is quarterly) by the sum of the unadjusted seasonal indexes. This ensures that the average seasonal index is one since all of the seasonal indexes must equal the number of periods in the year. If this were not done, error would be introduced into the final forecast.
The adjusted seasonal index is the product of the unadjusted seasonal index and the adjusting factor. A quarterly adjusted seasonal index of 0.942 suggests the data was 94.2 percent of the typical trend-cyclical value during the quarter. Accordingly, adjusted seasonal indexes greater than one indicate that the data was higher than the typical trend-cyclical values for that quarter.
To create the deseasonalized data, the original data values ( Y ) must be divided by their appropriate seasonal indexes ( S ). Once the deseasonalized data is computed, it can be analyzed to identify true fluctuations in the time series. These fluctuations can help management in strategic planning.
By using simple linear regression, the trend of the time series can be estimated. This process is done by using the deseasonalized values to create a trend-cyclical regression equation of the form Tt = a + bt…where t is equal to the period. Hence, t = 1 refers to year 1, quarter 1. Although actual simple linear regression computations are not shown, recommendations are to use Excel or Minitab when creating the trend-cyclical regression equations from the deseasonalized data.
Using the trend-cyclical regression equation, the trend data can be created by imputing each period’s assigned number into the equation. Note: At this point, it would be suitable to check the model to see how closely it fits the data. This process is omitted from this demonstration; however, in practice it should be performed before continuing. A demonstration of this is presented in … DeLurgio, Stephen, and Bhame, Carl. Forecasting Systems for Operations Management . Homewood: Business One Irwin, 1991. 296-297. The final forecast is developed by multiplying the trend values by their appropriate seasonal indexes. This produces a more accurate forecast for management. Note: As previously mentioned, this method is appropriate for short-term forecasts, but forecasts for periods longer than one year should include an adjustment for cyclical influences.
Steps summarized from … DeLurgio, Stephen, and Bhame, Carl. Forecasting Systems for Operations Management . Homewood: Business One Irwin, 1991. 297-298.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Use the hyperlink to navigate to the explanation slide that includes conceptual details in the notes.
Graphing the trend, original, and deseasonalized data can be very helpful for identifying fluctuations in trend. Deviations from the norm can be invaluable knowledge for management to analyze and use for planning future capacity, production, and allocations of resources.
This example provides individuals with the opportunity to apply the new skills they have learned through this presentation. It is highly recommended that a spreadsheet program such as Excel or Minitab be used for computations and for building the trend-cyclical regression equation. In Excel, simple linear regression can be performed by going to Tools , Data Analysis , and using the Regression tool. Preformatted Excel templates have been created for this exercise and are available in Appendix A. Solutions for all steps are presented in hidden slides in Appendix B.
Definitions taken from … StatSoft Inc. (2003). Time Series Analysis. Retrieved April 21, 2003, from http://www.statsoft.com/textbook/sttimser.html Time series models are based on the assumption that what has happened in the past will reoccur in the future. Classical decomposition can be used to segregate the elements of a time series model; after studying each component’s sub-patterns, management can apply the new learned knowledge when making decisions regarding strategic planning.
The sources provided in the bibliography and readings list are highly recommended to individuals wishing to expand their knowledge in classical decomposition and similar statistical tools.
Directions for use: Double-click on the desired table Highlight the cells of the table Select “copy” from the right-click pop-up menu or the Edit pull-down menu Open a spreadsheet program Paste the table into the spreadsheet program
Directions for use: Double-click on the desired table Highlight the cells of the table Select “copy” from the right-click pop-up menu or the Edit pull-down menu Open a spreadsheet program Paste the table into the spreadsheet program
Directions for use: Double-click on the desired table Highlight the cells of the table Select “copy” from the right-click pop-up menu or the Edit pull-down menu Open a spreadsheet program Paste the table into the spreadsheet program
Directions for use: Double-click on the desired table Highlight the cells of the table Select “copy” from the right-click pop-up menu or the Edit pull-down menu Open a spreadsheet program Paste the table into the spreadsheet program
Directions for use: Double-click on the desired table Highlight the cells of the table Select “copy” from the right-click pop-up menu or the Edit pull-down menu Open a spreadsheet program Paste the table into the spreadsheet program
To show these slides in the presentation: Select the Normal View tab In the left-hand screen, select slide From the Slide Show pull down menu, press Hide Slide
To show these slides in the presentation: Select the Normal View tab In the left-hand screen, select slide From the Slide Show pull down menu, press Hide Slide
To show these slides in the presentation: Select the Normal View tab In the left-hand screen, select slide From the Slide Show pull down menu, press Hide Slide
To show these slides in the presentation: Select the Normal View tab In the left-hand screen, select slide From the Slide Show pull down menu, press Hide Slide
To show these slides in the presentation: Select the Normal View tab In the left-hand screen, select slide From the Slide Show pull down menu, press Hide Slide