Section 1
##### Introduction to Analytics

1

Introduction to Excel

2

Conditional Formatting

3

Data Summarization techniques

4

Graphical summary using SAS/GRAPH: Introduction to Bar graph

5

Graphical summary using SAS/GRAPH: Introduction to Pie graph

6

Graphical summary using SAS/GRAPH introduction to Histogram, Box plots, Scatter diagram

7

Descriptive Statistics-Introduction to various measures of Central Tendency

8

Introduction to the measures of Dispersion, Range, Mean Deviation , Standard Deviation

Section 2
##### Understanding Probability and Probability Distribution

1

Introduction to Probability theory

2

Types of probability distribution – Discrete Distribution and Continuous distribution

3

Understanding Probability Mass Function and Probability Density Function

4

Normal Distribution and Standard Normal Distribution

5

Normal plot using Proc GPLOT procedure in SAS

6

Application of Normal distribution in Analytics with real life examples

7

Binomial Distribution and Binomial plot using PROC GPLOT procedure in SAS

8

Poisson distribution and Poisson plot using Proc GPLOT procedure in SAS

9

Application of Binomial and Poisson distribution in Analytics with real life examples

Section 3
##### Introduction to Sampling Theory and Estimation

1

Concept of Population and Sample

2

Use of PROC SURVEYSELECT procedure in SAS

3

Introduction to Some important terminologies

4

Parameter and Statistic

5

Properties of a good estimator

6

Standard Deviation and Standard Error

7

Point and Interval Estimation

8

Confidence level and level of Significance

9

Constructing Confidence Intervals

10

Formulation of Null and Alternative hypothesis

11

Performing simple test of Hypothesis

Section 4

Section 5
##### Statistical Significance of T-Tests Chi Square Tests and Analysis of Variance

1

Performing test of one sample mean using Proc ttest

2

Difference between two group means (independent sample) using Proc ttest

3

difference between two group means (Paired sample) using Proc ttest

4

Performing Chi-square tests: Test of Independence

5

Performing one-way ANOVA with PROC ANOVA and PROC GLM procedure

6

Performing post-hoc multiple comparisons tests in PROC

7

GLM using Tukey’s mean test

Section 6
##### Introduction to Segmentation Techniques: Factor Analysis

1

Introduction to Factor Analysis and various techniques

2

Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA)

3

Application of Factor Analysis using Proc Factor procedure

4

KMO MSA test, Bartlett’s Test Sphericity

5

The Mineigen Criterion, Scree plot

6

Introduction to Factor Loading Matrix

7

Various rotation techniques like Varimax

Section 7
##### Introduction to Segmentation Techniques: Cluster Analysis

1

Introduction to Cluster Analysis and various techniques

2

Hierarchical and Non – Hierarchical Clustering techniques

3

Using Hierarchical Clustering by Proc Tree procedure in SAS

4

Performing K – means Clustering in SAS

5

Divisive Clustering, Agglomerative Clustering

6

Application of Cluster Analysis in Analytics with profiling of the clusters and interpretation of the clusters

Section 8
##### Correlation and Linear Regression

1

Introduction to Pearson’s Correlation coefficient using PROC CORR procedure

2

Correlation and Causation – Fitting a simple linear regression model with the Proc REG procedure

3

Understanding the concepts of Multiple Regression

4

Using automated model selection techniques in PROC REG to choose the best model

5

Interpretation of the model: overall fit of the model and finding out the influential variables

6

Linear Regression diagnostics

7

Examining Residual

8

Assessing Collinearity, Heteroskedasticity and Auto – Correlation

Section 9
##### Introduction to Categorical Data Analysis and Logistic Regression

1

Comparison between Liner Regression and Logistic Regression

2

Performing Logistic regression using Proc Logistic Procedure in SAS

3

Performing Goodness of ft of the model

4

Introduction to Percent Concordant, AIC, SC, and Hosmer – Lemeshow

5

Receiver Operating Characteristics (ROC) Curve and Area under Curve (AUC)

6

Interpretation of the model: overall fit of the model and finding out the influential variables using Odds ratio criteria

7

Using automated model selection techniques in PROC Logistic to choose the best model using AIC criteria

Section 10
##### Introduction to Time Series Analysis

1

What is Time series Analysis, Objectives and Assumptions of Time Series

2

Identifying pattern in Time series data: Decomposition of the time series data and general aspect of the analysis

3

Introduction to Various Smoothing techniques: Simple Moving Average, Weighted Moving Average, Exponential Smoothing, Holt’s Linear Exponential Smoothing

4

Examples of Seasonality and detecting Seasonality in Time series data

5

Introduction to Proc Forecast to generate forecast for time series data

6

Autoregressive models and Stepwise Autoregression (STEPAR) procedure

7

Autoregressive and Moving Average models and Introduction to Box Jenkins Methodology

8

Introduction to Autoregressive Moving Average (ARMA) model

9

Autoregressive Integrated Moving Average (ARIMA) model

10

Building an ARIMA Model

11

Detection of Stationarity, Seasonality in ARIMA Model

12

Detecting the order of AR and MA of ARIMA model by Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF)

13

Detecting the order by using AIC and BIC criterion

14

Estimation and forecast using Proc ARIMA in SAS

Descriptive Statistics is the discipline of quantitatively describing the main features of a given data set. It provides simple summary measures about the sample about the observations that has been made in the set. These summary measures may form the basis of the initial description of a data as a part of a more extensive statistical analysis or they may suffice in themselves for some particular statistical investigations.

The most commonly used descriptive statistics in statistical analysis are:

**Measures of Central Tendency**, which yield a representative value for a set of observations.**Measures of Dispersion**, which show how different are the observations in a given data set different from the central value on an average.**Measures examining the shape of a given data distribution**.**Measures aimed at examining the most unusual observations of a data set**.

In this module we’ll learn about the different measures of central tendency.

**Measures of Central Tendency**

Central tendency refers to the propensity of quantitative data to cluster around a particular value. The particular value around which the observations in the data set fluctuate is called the central value. It is a representative value of the set of given observations. The objective of the analyst is to find out functional forms based on the observations of the data set which would give a ‘good’ representative central value. Such functional forms are known as measures of central tendency. The most widely used measures of central tendency are: Mean, Median and Mode.

For Example;

The vice president of marketing of a fast – food chain is studying the sales performance of the 100 stores in the eastern part of the country. He would be looking at the distribution with an eye toward getting information about the central tendency to compare the eastern part with other parts of country. Central tendency is basically the central most value of a distribution. Now how do we know which one is the central most value?

There are precisely three ways to find the central value: Mean, Median and Mode.

**Mean**

As a measure of central tendency, Mean gives the average value of a set of observations. The idea of average is a familiar one. Suppose, we say ‘Germans live longer than Indians’. This does not mean that every Germans live longer than every Indians. All we mean is that the longevity of a typical German is more than the average longevity of a typical Indian.

**Properties**

- The sum of the deviations of the given values of a variable from its mean is necessarily zero
- The Arithmetic Mean of a sample of observations depends both on the change of scale and origin.
- The combined Arithmetic Mean for two groups of with mean x1 and x2 and with n1 and n2 observations respectively is defined by

**Median**

Median of a set of statistical observations is the middlemost value of a data set when they are arranged in the increasing order of the magnitude. Median is that value of the variable which divides the group into two equal parts, one comprising all the values greater and the other, all values less than median.

**Properties**

Based on the construction and the nature of operation Median, as a measure of central tendency exhibits the following important properties:

- Median obeys linearity, i.e. it depends simultaneously on the change of scale and origin.
- The combined median of the two groups lies in between the median of the two individual groups.

**Mode**

Mode, for a given set of observations is that value of the variable, where the variable occurs with considered to represent the true characteristics of a frequency distribution and it is referred as the most typical or the fashionable value of the variate.