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**Managerial Statistics**

Managerial statistics is mainly concerned with formulating and identifying statistical problems in business decision making by using the application of statistics. It mainly focuses on the business applications of hypothesis testing.

In business, decisions that are made by the modern managers need the arrangements of statistical skills, such as collecting and identifying data, building experiments, developing regression models, six sigma, etc. these all are the important capabilities that must be utilized by a manager before making decision.

Managerial Statistics deals with the various topics, such as discrete and continuous random variables, sampling, sampling and sampling distributions, confidence intervals, quality improvement, hypothesis testing, regression analysis, linear regression, descriptive statistics, portfolio management, elementary probability theory, etc.

IBM SPSS Statistics is the majorly used software of Managerial Statistics. It involves various products that represent the whole analytical process, such as planning, data collection, analysis, deployment and reporting. It comes with a base version and also has three different editions. Its base version is known as SPSS Statistics Base which includes a wide range of statistical procedures, such as linear regression, Monte Carlo Simulation, etc. to solve many problems. Three different editions of IBM SPSS Statistics software are as follows:

- SPSS Statistics Professional
- SPSS Statistics Premium
- SPSS Statistics Standard

Statistical Inference refers to a process which analyzes the data first to estimate the characteristics of population. On the basis of the observed results, it enables user to infer the conclusions. Inferential Statistical analysis involves deriving estimates and testing hypothesis to infer the properties of the population. Statistical Inference is based on the probability law which involves the two main terms:

- Parameter: parameter refers to a numeric number which tells about the population in the terms of proportion or percentage.
- Statistic: in this, a user doesn’t need know about the any unknown parameters. It refers to a number that can be calculated from the observed data.

Regression analysis mainly used to observe the relationship between independent variable and dependent variable. It used in the various areas, such as time series modeling, forecasting, etc. it defines the two kind of relation between independent and dependent variables:

- Signification relationship among both
- Impact of the independent variable on the dependent variable

Correlation is one which is used to describe the degrees of relationship among two variables. Correlation coefficient is one which is used to measure the degrees between two related variables. Its signs represent the way of the association and its magnitude represents the strength of the association. In positive Correlation coefficient, value of the variables increased or decreased in pair and in negative Correlation coefficient, value of the one variable increase and value of the other variable decrease.

Data Distributions are mainly used in the statistics. Data distributions refer to the graphical methods that used to manage and organize the convenient information and data distribution statistics used by the query optimizer and it is stored in the system catalog. Query optimizer used data distribution statistics at the time of the designing of query execution plans. There are some system Catalog Tables that is available to the query optimizer and stores data distribution information are as follows:

- SYSDISTRIB
- SYSFRAGDIST

Six Sigma is major concept that involved in the Managerial statistics. In many organizations, it used to eliminate the defects and measure the quality of process which leads to the perfection. Main aim of Six Sigma is to enhance the performance of the process through its applications. Main two sub- methodologies of Six Sigma are DMAIC and DMADV. If a process contains only one specification limit i.e. lower or upper then it provides the resultant output is Six Sigma i.e. this generate six process standard deviation among the customer needs and process. But if a process contains more than one specification limit then its resultant output will not be Six Sigma because it produces more than one six process standard deviation.

In Multiple Regression, a user mainly used the two variables, one is dependent which is that a user wants to predict or the other one is independent variable that is used by the user to predict the dependent variable. Multiple Regression enables user to define the whole variance of the model and respective contribution.

Wilcoxon signed-rank test is defined as the nonparametric test which is identical to the dependent t-test. Two sets that are from the identical participants can be compared by using Wilcoxon signed-rank test. This test is mainly used by the user when the use of the dependent t-test is unsuitable.

Furthermore, Managerial statistics subject covers the various concepts, including Variance Analysis and Design, interval estimation, graphical descriptions of data, descriptive statistics, simple and multiple linear regression, and so on. Some of the progressive topics that cover by the Managerial statistics subject are listed below:

- Simple Regression Model
- Residual Analysis
- Nominal Independent Variables
- Multicollinearity
- NonParametric Statistics
- Chi-Squared Goodness of Fit Test
- Kruskall-Wallis Test
- Spearman Rank Correlation Coefficient

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**Data and Statistics**

- Descriptive Statistics:, Tabular and Graphical Presentation, Descriptive Statistics: Numerical measure, Probability, Discrete Probability Distribution, Continuous Probability Distribution, Sampling, Sampling Distribution, Descriptive Statistics, Probability, Random Variables and their Distributions, and Normal Distribution , Sampling and Estimation.
- Sampling Distributions, and Estimation and Confidence Intervals, Linear Regression, simple linear regression, Multiple linear regression + dummy variables, model estimation, forecasting via regression, non-linear regression, Probabilistic Thinking, Descriptive Statistics, PivotTable, Basics of Probability, Conditional Probability, Expected Value and Variance of a Probability Distribution.
- Binomial Distribution, Decision Analysis, Normal Distribution, Normal, Basics of Portfolio Analysis, Correlation and Covariance, More Portfolios, Central Limit Theorem, Normal Approximation to the Binomial, Sampling Theory, Confidence Intervals for Single Populations, Student's t Distribution, Polling Examples, Confidence Intervals for Two Populations, Sample Size Selection, Basic Hypothesis Testing.
- Hypothesis Testing for Multiple Populations, Simple Regression, Multiple Regression, Multiple Regression: Model Building and Validation, Multicollinearity, Heteroscedasticity, Non-normality of Errors.

**Topics for Managerial Statistics**

- Descriptive Statistics, recap of descriptive statistics, mean, median, standard deviation, Normal approximation, Value-at-Risk, Normal approximation, financial data, regression line, correlation, causation , Random variables, expected value.
- variance, Normal Distribution, Normal distribution, normal table, linear transformations, hedging, portfolios, Sampling Distributions, Estimation, Confidence Intervals, Hypothesis Testing, Sampling proportions.
- interpreting opinion pollsHypothesis Testing, structure of a test for the population mean, Linear regression, simple linear regression, Multiple linear regression,