Correlation Analysis: Introduction, definition, utility, types, properties, and degree of correlation, correlation and causation. Measures of coefficient of correlation; Scatter diagram, Karl Pearson’s methods (Deviation method, Product moment method, Variance-Covariance method), Probable error and Karl Pearson’s method of coefficient of correlation. Spearman’s Rank correlation method ( when ranks are given, when ranks are not given, equal or tied ranks), coefficient of determination.
Regression Analysis: Meaning, definition, utility of regression. Comparison between correlation and regression. Two lines of regression; Regression equation of line Y on X, Regression equation of line X on Y, Properties of regression lines. Relationship between correlation and regression coefficient.
Time Series Analysis: Meaning, definition and utility of time series. Component of time series (Trend, Seasonal variations, Cyclical variations, Irregular variations), Decomposition of time series. Linear trend analysis using freehand method and least square method.
SAS Programming and Data Analysis Portfolio - BTReillyBrian Reilly
This document is a portfolio submitted by Brian Thomas Reilly to Florida State University containing projects analyzing transportation security administration (TSA) claims data from 2002 to 2014 using SAS software. The portfolio includes a project on SAS for data analysis that analyzes the TSA claims data, performing graphical and numerical summaries, statistical tests, and drawing conclusions. It finds that on average, it is better financially to lose an item at a TSA checkpoint than in checked baggage, with the average compensation per loss being over $107 higher at checkpoints. The source code for importing, cleaning, and merging the claims data files is also included.
This document analyzes the relationship between stock market liquidity and stock returns in 27 emerging equity markets from January 1992 to December 1999. It finds that stock returns are positively correlated with measures of market liquidity, including turnover ratio, trading value, and turnover-volatility multiple, in both cross-sectional and time-series analyses. This relationship holds even after controlling for other factors and contrasts with theories supported by studies of developed markets, where liquidity and returns are negatively correlated. The findings suggest emerging markets have a lower degree of integration with the global economy.
This document summarizes a study that estimated the beta of Costco Wholesale Corporation stock using the Capital Asset Pricing Model. The authors collected quarterly stock price data for Costco and the S&P 500 index over a 10-year period. They performed a linear regression of Costco's returns against the market risk premium (S&P 500 returns - risk-free rate). The regression estimated Costco's beta at 0.642, meaning its returns tend to be about 64.2% as volatile as the overall market. However, the regression had a low R-squared value, indicating the model was not a great fit for the data. Therefore, while beta provides some insight into risk, other factors like
Predicting Stock Market Returns and the Efficiency Market HypothesisMysa Vijay
There has been growing interest on financial forecasting in recent years as accurate
forecasting of financial prices has become an important issue in investment decision making
Lu et al. (2009). It is argued that exchange rate market is very efficient (Ince and Trafalis
2006). By predicting the accurate results in return, it gives the opportunity for investors to
make profitable decisions for investing their money. As many of the researchers argue that
efficiency market hypothesis theory is not true.
Investors of the stock market are “rational” and they adapt easily to recent knowledge
regarding the stock market products, which implies investors opinion in the market follow the
effects of any information revealed. This efficient market hypothesis contains three different
levels of information sharing: the weak form, the semi-strong form, and the strong form Fama
and French (2009). Many trials have been made to calculate the movements of stock markets
using quantitative information (Andersen et al. 2007; Fama and French 2009; Nartea 2009),
but some other studies state that stock market movements cannot be captured by firm‟s
quantitative information Shleifer and Vishny (1997). This is because the actual market is not
as efficient as the expressed by the theory of efficiency market hypothesis.
We want to investigate the above addressed problem as we want to see if can predict stock
market returns and test the theory of efficiency market hypothesis. We want to see if we can
predict the stock market returns in future and see how accurate we are in predicting in it.
After predicting we want to test the theory on efficiency market hypothesis on the predicted
values, as the market is not as efficient as expressed by efficiency market hypothesis.
In order to reach our goal, we selected three papers as our base line papers. Our aim is follow
their methodologies and their algorithms and predict the stock market returns. We implement
and reproduce the efforts done by Lu et al. (2009), Khansa and Liginlal (2009) and Ince and
Trafalis (2006). We want to know how close the mentioned authors‟ results were to the actual
data. In addition to that, we also want to know how close we are to the actual data.
This document discusses a research project investigating investor perception of mutual funds and their behavior using time series models. It provides background on the project, which analyzed daily net asset values for 30 mutual fund schemes from equity, debt and balanced categories over one year. The objectives were to study how personal and risk factors affect fund benefits and performance, and determine the causal relationship between benchmark indices and different fund schemes. The methodology section describes collecting primary data through a survey and secondary data from sources like AMFI. Variables for analysis included performance rating based on past performance, current NAV, and agency ratings. The analysis would use factor analysis, regression, and time series models.
Any business and economic applications of forecasting involve time series data. Re-gression models can be fit to monthly, quarterly, or yearly data using the techniques de-scribed in previous chapters. However, because data collected over time tend to exhibit trends, seasonal patterns, and so forth, observations in different time periods are re¬lated or autocorrelated. That is, for time series data, the sample of observations cannot be regarded as a random sample. Problems of interpretation can arise when standard regression methods are applied to observations that are related to one another over time. Fitting regression models to time series data must be done with considerable care.
Report earned 105% and is a complete valuation of the company based upon CAPM and the Dividend Discount Models. Includes regression analysis of macro variables, figures from conference calls and 10Ks, and a fair market stock price. (Not to be used as investment advice)
SAS Programming and Data Analysis Portfolio - BTReillyBrian Reilly
This document is a portfolio submitted by Brian Thomas Reilly to Florida State University containing projects analyzing transportation security administration (TSA) claims data from 2002 to 2014 using SAS software. The portfolio includes a project on SAS for data analysis that analyzes the TSA claims data, performing graphical and numerical summaries, statistical tests, and drawing conclusions. It finds that on average, it is better financially to lose an item at a TSA checkpoint than in checked baggage, with the average compensation per loss being over $107 higher at checkpoints. The source code for importing, cleaning, and merging the claims data files is also included.
This document analyzes the relationship between stock market liquidity and stock returns in 27 emerging equity markets from January 1992 to December 1999. It finds that stock returns are positively correlated with measures of market liquidity, including turnover ratio, trading value, and turnover-volatility multiple, in both cross-sectional and time-series analyses. This relationship holds even after controlling for other factors and contrasts with theories supported by studies of developed markets, where liquidity and returns are negatively correlated. The findings suggest emerging markets have a lower degree of integration with the global economy.
This document summarizes a study that estimated the beta of Costco Wholesale Corporation stock using the Capital Asset Pricing Model. The authors collected quarterly stock price data for Costco and the S&P 500 index over a 10-year period. They performed a linear regression of Costco's returns against the market risk premium (S&P 500 returns - risk-free rate). The regression estimated Costco's beta at 0.642, meaning its returns tend to be about 64.2% as volatile as the overall market. However, the regression had a low R-squared value, indicating the model was not a great fit for the data. Therefore, while beta provides some insight into risk, other factors like
Predicting Stock Market Returns and the Efficiency Market HypothesisMysa Vijay
There has been growing interest on financial forecasting in recent years as accurate
forecasting of financial prices has become an important issue in investment decision making
Lu et al. (2009). It is argued that exchange rate market is very efficient (Ince and Trafalis
2006). By predicting the accurate results in return, it gives the opportunity for investors to
make profitable decisions for investing their money. As many of the researchers argue that
efficiency market hypothesis theory is not true.
Investors of the stock market are “rational” and they adapt easily to recent knowledge
regarding the stock market products, which implies investors opinion in the market follow the
effects of any information revealed. This efficient market hypothesis contains three different
levels of information sharing: the weak form, the semi-strong form, and the strong form Fama
and French (2009). Many trials have been made to calculate the movements of stock markets
using quantitative information (Andersen et al. 2007; Fama and French 2009; Nartea 2009),
but some other studies state that stock market movements cannot be captured by firm‟s
quantitative information Shleifer and Vishny (1997). This is because the actual market is not
as efficient as the expressed by the theory of efficiency market hypothesis.
We want to investigate the above addressed problem as we want to see if can predict stock
market returns and test the theory of efficiency market hypothesis. We want to see if we can
predict the stock market returns in future and see how accurate we are in predicting in it.
After predicting we want to test the theory on efficiency market hypothesis on the predicted
values, as the market is not as efficient as expressed by efficiency market hypothesis.
In order to reach our goal, we selected three papers as our base line papers. Our aim is follow
their methodologies and their algorithms and predict the stock market returns. We implement
and reproduce the efforts done by Lu et al. (2009), Khansa and Liginlal (2009) and Ince and
Trafalis (2006). We want to know how close the mentioned authors‟ results were to the actual
data. In addition to that, we also want to know how close we are to the actual data.
This document discusses a research project investigating investor perception of mutual funds and their behavior using time series models. It provides background on the project, which analyzed daily net asset values for 30 mutual fund schemes from equity, debt and balanced categories over one year. The objectives were to study how personal and risk factors affect fund benefits and performance, and determine the causal relationship between benchmark indices and different fund schemes. The methodology section describes collecting primary data through a survey and secondary data from sources like AMFI. Variables for analysis included performance rating based on past performance, current NAV, and agency ratings. The analysis would use factor analysis, regression, and time series models.
Any business and economic applications of forecasting involve time series data. Re-gression models can be fit to monthly, quarterly, or yearly data using the techniques de-scribed in previous chapters. However, because data collected over time tend to exhibit trends, seasonal patterns, and so forth, observations in different time periods are re¬lated or autocorrelated. That is, for time series data, the sample of observations cannot be regarded as a random sample. Problems of interpretation can arise when standard regression methods are applied to observations that are related to one another over time. Fitting regression models to time series data must be done with considerable care.
Report earned 105% and is a complete valuation of the company based upon CAPM and the Dividend Discount Models. Includes regression analysis of macro variables, figures from conference calls and 10Ks, and a fair market stock price. (Not to be used as investment advice)
The document discusses the derivation and testing of the Capital Asset Pricing Model (CAPM). It begins by restating three key equations related to the CAPM. It then describes the assumptions and derivation of the CAPM, noting that the key insight is that the market portfolio is efficient. The document outlines how the CAPM makes testable predictions about asset expected returns and betas. It discusses additional assumptions required to test the CAPM using regression analysis. Specifically, it explains the Fama-MacBeth and Gibbons-Ross-Shanken (GRS) approaches to estimating the security market line implied by the CAPM using cross-sectional and time-series regressions respectively.
Efficient Frontier Searching of Fixed Income Portfolio under CROSSSun Zhi
This document describes a framework for constructing efficient frontiers for fixed income portfolios under China's CROSS (China Risk Oriented Solvency System) regulatory framework. The framework uses quadratic programming to optimize portfolios to meet expected yield targets while staying within regulatory capital limits. A simulation case examines efficient frontiers with and without duration constraints. It finds that holding long-duration corporate bonds to maturity uses less regulatory capital than trading them. The framework allows insurance firms to maximize returns within capital limits by providing optimal asset allocations.
The document summarizes the capital asset pricing model (CAPM) and reviews early empirical tests of the model. It begins by outlining the logic and key assumptions of the CAPM, including that the market portfolio must be mean-variance efficient. However, empirical tests found problems with the CAPM's predictions about the relationship between expected returns and market betas. Specifically, cross-sectional regressions did not find intercepts equal to the risk-free rate or slopes equal to the expected market premium. To address measurement error, later tests examined portfolios rather than individual assets. In general, the early empirical evidence revealed shortcomings in the CAPM's ability to explain returns.
Capital structure Analysis of Indian Oil Corporation Limited (IOCL)Kangkan Deka
The document discusses the capital structure analysis of Indian Oil Corporation Limited (IOCL). It provides background information on IOCL, describing it as India's largest company by sales. The document outlines IOCL's vision, mission and values. It then discusses the methodology used for the capital structure analysis, which involves analyzing data from IOCL's annual reports. Various components of IOCL's capital structure are examined, including share capital, paid-up capital, long-term debt and leverage ratios.
Impact of capital asset pricing model (capm) on pakistanAlexander Decker
This document summarizes a research study that applied the Capital Asset Pricing Model (CAPM) to stocks traded on the Karachi Stock Exchange in Pakistan from 2003 to 2007. The study found that CAPM was able to estimate stock returns in the Pakistani market and showed the existence of a risk premium as the only factor affecting stock returns. The study used monthly return data from 5 portfolios sorted by size and book-to-market ratios. Regression analysis found the intercept was insignificant while the risk premium was significant, showing CAPM estimates stock returns accurately in this market. However, the study notes CAPM has limitations and future research could test different models or variations to further analyze factors affecting stock returns.
A project report on portfolio managementProjects Kart
Portfolio management involves managing a group of investments to meet organizational goals and reduce risk. It includes deciding which investments to select and fund, and which to discontinue. The document discusses how portfolio management applies to managing software applications, products, and initiatives within an organization. It aims to maximize returns and diversify investments across different asset classes or types of projects.
7 QC Tools PDF | An eBook with A Detailed Description and Practical ExamplesShakehand with Life
The document describes a book about 7 quality control tools. It includes an introduction to each of the 7 tools: process flow diagram, check sheet, histogram, Pareto diagram, cause-and-effect diagram, scatter diagram, and control charts. For each tool it provides details on what it is, how to construct it, examples, and how to construct the tool in Microsoft Excel. It also includes an introduction to Kaizen and 5S, practice problems, a test, and answers.
Activity network diagram helps to schedule a project efficiently. It gives an idea of the minimum and maximum time to complete a project. The 7th tool among the New 7 management development tool.
Process Decision and Program is designed to achieve a particular objective. Used especially in new process development. The tool avoids surprises and identifies the possible countermeasures.
Prioritization matrix prioritizes issues, based on weighted criteria using a combination of Tree and Matrix diagram. It is a very important tool for the management to prioritize the issue to work on.
Interrelationship digraph is another important tool out of New 7 Quality Tools. It helps to clarify the interrelationship of many factors of a complex situation. It identifies key drivers and the key outcomes.
New 7 QC Tools; Affinity diagram, Interrelationship digraph, Tree diagram, Matrix diagram, Prioritization matrices, Process Decision and Program Chart (PDPC), and Activity Network Diagram. The New 7 QC Tools also known as 7 Management Development Tools. These tools unlike the 7 fundamentals quality control tools, process the subjective data and help the management to make the better decision, regarding project management and quality improvement.
The affinity diagram is one among the New 7 Quality Contol tools, helps to categorize the same type of ideas or issues. Affintiy diagram process the same type of subjective data in a particular category.
Course Catalog 2016-17, is the overview of various corporate trainings courses for our deemed clientele, so that they can lock the dates for in-house training facilitation at company site in the year of 2016-17.
7 QC Tools and SPC Training Dec.2015. Send nominations before 15 Nov. 2015 and get an attractive discount for early birds. Group discount for 5 or more is also available. For nomination form or call; 9468267324, 8684861131, e-mail shakehandwithlife@gmail.com,
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
Narender Sharma is an Indian quality professional and corporate trainer. He has over 15 years of experience in quality control and has trained on topics like 7 QC tools, Six Sigma, and ISO standards. He runs his own corporate training business and has authored several e-books on quantitative techniques and quality management. Sharma aims to provide training to 20,000 professionals and students by 2020 through online courses and in-person seminars. He is passionate about social causes like honoring Indian independence activists and strives to spread their messages to younger generations.
Go through the seven quality tools training quiz and compare, how much you have learnt from this online training of 7QC tools? The quiz has 15 multiple choice questions based on seven quality tools. Choose one answer out of the given choices for every question write these choices on a paper. After completing the quiz compare yourself with answer key in the end of quiz. Find yourself where you are in learning of 7 QC Tools. If you find your performance is not up to the mark then go again for the training of seven QC tools. You may do it as many times as you want. Improve your performance every time you go through the training.
Seven QC Tools Training; Control Charts (Mean Chart and Range Chart)Shakehand with Life
Seven quality tools training is incomplete without learning of control charts. Control charts help to control the process with in the set control limits. Control charts are mainly two types; Mean Chart and Range Chart. Mean chart showcase the process data complied by the designated person and signal when the data go beyond the control limits. Every process has variation and due to this variation data get fluctuated. This fluctuation shown on the mean and range chart by data points. The causes of fluctuation in the data are assignable and common causes. Due to common causes data fluctuated around the average of the data but due to assignable cause data go beyond the control limits. When data go beyond the control limits control charts warn the operator that something is going wrong in the process and need to special attention. Mean chart is the spread of the mean values of the samples around the mean line. Range chart is spread of the range of samples around the mean line of range.
Scatter diagram is the graphical presentation of relationship between two variables. Scatter diagram is an important tool out of 7 fundamental tools of quality control. Scatter diagram helps to confirm the degree of relationship between cause and effect. Here cause is an independent variable and effect is dependent variable. Scatter diagram is an important statistical tool to analyze the relationship of two variables. To create the scatter diagram take the values of independent variable on X-Axis where as the dependent variable is taken on Y-Axis. Plot the intersection points of X and Y on the graph. Draw a straight line passing through all the points. Analyze the pattern of the points. For different degree of relationship different pattern of scatter diagram is formed. If Y increases as X increases and data points are on the straight line then there is perfect positive correlation. If Y decreases with increase of X and data points are on the straight line then there is perfect negative correlation. But when data is scattered all over the graph then there is zero correlation.
The document discusses the derivation and testing of the Capital Asset Pricing Model (CAPM). It begins by restating three key equations related to the CAPM. It then describes the assumptions and derivation of the CAPM, noting that the key insight is that the market portfolio is efficient. The document outlines how the CAPM makes testable predictions about asset expected returns and betas. It discusses additional assumptions required to test the CAPM using regression analysis. Specifically, it explains the Fama-MacBeth and Gibbons-Ross-Shanken (GRS) approaches to estimating the security market line implied by the CAPM using cross-sectional and time-series regressions respectively.
Efficient Frontier Searching of Fixed Income Portfolio under CROSSSun Zhi
This document describes a framework for constructing efficient frontiers for fixed income portfolios under China's CROSS (China Risk Oriented Solvency System) regulatory framework. The framework uses quadratic programming to optimize portfolios to meet expected yield targets while staying within regulatory capital limits. A simulation case examines efficient frontiers with and without duration constraints. It finds that holding long-duration corporate bonds to maturity uses less regulatory capital than trading them. The framework allows insurance firms to maximize returns within capital limits by providing optimal asset allocations.
The document summarizes the capital asset pricing model (CAPM) and reviews early empirical tests of the model. It begins by outlining the logic and key assumptions of the CAPM, including that the market portfolio must be mean-variance efficient. However, empirical tests found problems with the CAPM's predictions about the relationship between expected returns and market betas. Specifically, cross-sectional regressions did not find intercepts equal to the risk-free rate or slopes equal to the expected market premium. To address measurement error, later tests examined portfolios rather than individual assets. In general, the early empirical evidence revealed shortcomings in the CAPM's ability to explain returns.
Capital structure Analysis of Indian Oil Corporation Limited (IOCL)Kangkan Deka
The document discusses the capital structure analysis of Indian Oil Corporation Limited (IOCL). It provides background information on IOCL, describing it as India's largest company by sales. The document outlines IOCL's vision, mission and values. It then discusses the methodology used for the capital structure analysis, which involves analyzing data from IOCL's annual reports. Various components of IOCL's capital structure are examined, including share capital, paid-up capital, long-term debt and leverage ratios.
Impact of capital asset pricing model (capm) on pakistanAlexander Decker
This document summarizes a research study that applied the Capital Asset Pricing Model (CAPM) to stocks traded on the Karachi Stock Exchange in Pakistan from 2003 to 2007. The study found that CAPM was able to estimate stock returns in the Pakistani market and showed the existence of a risk premium as the only factor affecting stock returns. The study used monthly return data from 5 portfolios sorted by size and book-to-market ratios. Regression analysis found the intercept was insignificant while the risk premium was significant, showing CAPM estimates stock returns accurately in this market. However, the study notes CAPM has limitations and future research could test different models or variations to further analyze factors affecting stock returns.
A project report on portfolio managementProjects Kart
Portfolio management involves managing a group of investments to meet organizational goals and reduce risk. It includes deciding which investments to select and fund, and which to discontinue. The document discusses how portfolio management applies to managing software applications, products, and initiatives within an organization. It aims to maximize returns and diversify investments across different asset classes or types of projects.
7 QC Tools PDF | An eBook with A Detailed Description and Practical ExamplesShakehand with Life
The document describes a book about 7 quality control tools. It includes an introduction to each of the 7 tools: process flow diagram, check sheet, histogram, Pareto diagram, cause-and-effect diagram, scatter diagram, and control charts. For each tool it provides details on what it is, how to construct it, examples, and how to construct the tool in Microsoft Excel. It also includes an introduction to Kaizen and 5S, practice problems, a test, and answers.
Activity network diagram helps to schedule a project efficiently. It gives an idea of the minimum and maximum time to complete a project. The 7th tool among the New 7 management development tool.
Process Decision and Program is designed to achieve a particular objective. Used especially in new process development. The tool avoids surprises and identifies the possible countermeasures.
Prioritization matrix prioritizes issues, based on weighted criteria using a combination of Tree and Matrix diagram. It is a very important tool for the management to prioritize the issue to work on.
Interrelationship digraph is another important tool out of New 7 Quality Tools. It helps to clarify the interrelationship of many factors of a complex situation. It identifies key drivers and the key outcomes.
New 7 QC Tools; Affinity diagram, Interrelationship digraph, Tree diagram, Matrix diagram, Prioritization matrices, Process Decision and Program Chart (PDPC), and Activity Network Diagram. The New 7 QC Tools also known as 7 Management Development Tools. These tools unlike the 7 fundamentals quality control tools, process the subjective data and help the management to make the better decision, regarding project management and quality improvement.
The affinity diagram is one among the New 7 Quality Contol tools, helps to categorize the same type of ideas or issues. Affintiy diagram process the same type of subjective data in a particular category.
Course Catalog 2016-17, is the overview of various corporate trainings courses for our deemed clientele, so that they can lock the dates for in-house training facilitation at company site in the year of 2016-17.
7 QC Tools and SPC Training Dec.2015. Send nominations before 15 Nov. 2015 and get an attractive discount for early birds. Group discount for 5 or more is also available. For nomination form or call; 9468267324, 8684861131, e-mail shakehandwithlife@gmail.com,
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
Narender Sharma is an Indian quality professional and corporate trainer. He has over 15 years of experience in quality control and has trained on topics like 7 QC tools, Six Sigma, and ISO standards. He runs his own corporate training business and has authored several e-books on quantitative techniques and quality management. Sharma aims to provide training to 20,000 professionals and students by 2020 through online courses and in-person seminars. He is passionate about social causes like honoring Indian independence activists and strives to spread their messages to younger generations.
Go through the seven quality tools training quiz and compare, how much you have learnt from this online training of 7QC tools? The quiz has 15 multiple choice questions based on seven quality tools. Choose one answer out of the given choices for every question write these choices on a paper. After completing the quiz compare yourself with answer key in the end of quiz. Find yourself where you are in learning of 7 QC Tools. If you find your performance is not up to the mark then go again for the training of seven QC tools. You may do it as many times as you want. Improve your performance every time you go through the training.
Seven QC Tools Training; Control Charts (Mean Chart and Range Chart)Shakehand with Life
Seven quality tools training is incomplete without learning of control charts. Control charts help to control the process with in the set control limits. Control charts are mainly two types; Mean Chart and Range Chart. Mean chart showcase the process data complied by the designated person and signal when the data go beyond the control limits. Every process has variation and due to this variation data get fluctuated. This fluctuation shown on the mean and range chart by data points. The causes of fluctuation in the data are assignable and common causes. Due to common causes data fluctuated around the average of the data but due to assignable cause data go beyond the control limits. When data go beyond the control limits control charts warn the operator that something is going wrong in the process and need to special attention. Mean chart is the spread of the mean values of the samples around the mean line. Range chart is spread of the range of samples around the mean line of range.
Scatter diagram is the graphical presentation of relationship between two variables. Scatter diagram is an important tool out of 7 fundamental tools of quality control. Scatter diagram helps to confirm the degree of relationship between cause and effect. Here cause is an independent variable and effect is dependent variable. Scatter diagram is an important statistical tool to analyze the relationship of two variables. To create the scatter diagram take the values of independent variable on X-Axis where as the dependent variable is taken on Y-Axis. Plot the intersection points of X and Y on the graph. Draw a straight line passing through all the points. Analyze the pattern of the points. For different degree of relationship different pattern of scatter diagram is formed. If Y increases as X increases and data points are on the straight line then there is perfect positive correlation. If Y decreases with increase of X and data points are on the straight line then there is perfect negative correlation. But when data is scattered all over the graph then there is zero correlation.
Process flow chart or Flow process chart among the seven quality control tools considered as the first and base of application of every quality tool. Process flow chart is the pictorial representations of all activities of process using different shape of boxes. Process flow chart is the guiding map of the whole process. With a single view, process flow chart gives almost every information about the whole process. Process flow diagram inform the starting and end point of the process along with the operations, decision, storage, delay, direction etc. through which the product or service passing. Different shapes like circle, rectangular circle, diamond, rectangle, arrows, D shapes, inverted rectangles etc. are used to construct process flow diagram. Process flow diagram clearly explains which operation is followed by which operation. Process flow chart helps to find out the potential trouble spots in the process so that corrective action can be taken to remove the hurdles at an early stage. To audit the whole process, process flow chart plays a vital role. Even for the new comers in the organization, process flow chart is an opportunity to understand their process easily.
Visit www.shakehandwithlife.in to buy this Book. This E-Book on 7QC tools is complete training workshop for Junior, Middle and Senior quality quality professionals. The USP of this workshop is the text and graphics in the book for understanding the tools while applying to solve the practial problems. Illustrative worked examples , Construction of tools in Excel like Histogram, Pareto Chart, Scatter Diagram, Control charts are beautifully explained in step step manner. A newcomer in the area of quality can easily understand how the tools be used and applied.
Measure of dispersion part II ( Standard Deviation, variance, coefficient of ...Shakehand with Life
This tutorial gives the detailed explanation measure of dispersion part II (standard deviation, properties of standard deviation, variance, and coefficient of variation). It also explains why std. deviation is used widely in place of variance. This tutorial also teaches the MS excel commands of calculation in excel.
Measure of dispersion part I (Range, Quartile Deviation, Interquartile devi...Shakehand with Life
This tutorial gives the detailed explanation of "Measure of Dispersion" (Range, Quartile Deviation, Interquartile Range, Mean Deviation) with suitable illustrative example with MS Excel Commands of calculation in excel.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
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This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
1. ShakehandwithLife.in
Quantitative Techniques
Volume-4
(Revised)
1. Correlation and Regression analysis
2. Time series analysis(Measurement of Linear Trend and Seasonal Variations)
E-Book Code : QTVOL4
by
Narender Sharma
“Save Paper, Save Trees, Save Environment”
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www.shakehandwithlife.in
E-mail : shakehandwithlife@gmail.com , narender@shakehandwithlife.in
Click on Contents
Correlation Analysis ........................................................................................................................................................................................ 3
Introduction .............................................................................................................................................................................................. 3
Definition of Correlation ...................................................................................................................................................................... 3
Utility of Correlation .............................................................................................................................................................................. 3
Types of Correlation .............................................................................................................................................................................. 3
Properties of Correlation ..................................................................................................................................................................... 5
Degree of Correlation:........................................................................................................................................................................... 6
Correlation and Causation .................................................................................................................................................................. 6
Measures of Coefficient of Correlation .................................................................................................................................................... 7
Scatter Diagram ............................................................................................................................................................................................ 7
Karl Pearson Coefficient of Correlation .............................................................................................................................................. 9
Deviation Method: .................................................................................................................................................................................. 9
Product Moment Method: ................................................................................................................................................................ 10
Variance – Covariance Method ....................................................................................................................................................... 10
Probable Error and Karl Pearson’s Coefficient of Correlation .......................................................................................... 11
Spearman’s Rank Correlation Method ............................................................................................................................................. 12
Rank Correlation coefficient when Ranks are given ............................................................................................................. 12
Rank Correlation coefficient when Ranks are not given ..................................................................................................... 13
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When equal or tied ranks ................................................................................................................................................................. 13
Coefficient of Determination................................................................................................................................................................ 15
Regression Analysis ...................................................................................................................................................................................... 17
Regression (Meaning) ....................................................................................................................................................................... 17
Definition of Regression.................................................................................................................................................................... 17
Utility of Regression ........................................................................................................................................................................... 17
Comparison Between Correlation and Regression ................................................................................................................ 17
Two Lines of Regression ........................................................................................................................................................................ 17
Regression equation of line y on x. ............................................................................................................................................... 17
Regression equation of line x on y ................................................................................................................................................ 17
Properties of regression Lines ....................................................................................................................................................... 18
Relationship between Correlation and Regression Coefficient ............................................................................................. 19
Time series analysis ..................................................................................................................................................................................... 22
Meaning of Time Series ..................................................................................................................................................................... 22
Definitions of Time Series ................................................................................................................................................................ 22
Utility of Time Series .......................................................................................................................................................................... 22
Components of Time Series ............................................................................................................................................................. 22
Analysis or Decompositions of Time Series .............................................................................................................................. 23
Measuring Linear Trends ..................................................................................................................................................................... 24
Free hand curve method ................................................................................................................................................................... 24
Least Square Method .......................................................................................................................................................................... 25
Fitting Straight Line Trend ............................................................................................................................................................. 25
Measurement of Seasonal Variations ............................................................................................................................................... 27
Simple Averages Method .................................................................................................................................................................. 27
References ........................................................................................................................................................................................................ 29
Feedback ........................................................................................................................................................................................................... 29
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Correlation Analysis
Introduction
Consider the following statement
“ Price of a commodity rises as the demand goes up.”
“Temperature rises as the intensity of sunlight increases.”
The above statement are very true. Price with demand and temperature with sunlight have direct or linear relation. Here demand and sunlight are independent variable and price and temperature are dependent variables.
But what degree the price is related to demand and what degree the temperature is related to the intensity of sunlight is the question of discussion.
In the above example one is independent (demand and intensity) and other one is dependent(Price and Temperature) hence,
The correlation gives an indication of how well the two variables move together in a straight line manner. The correlation between X and Y is the same as the correlation between Y and X.
Correlation for a sample is indicated by correlation coefficient(r).
Definition of Correlation
On the bases of above discussion we can define the Correlation as
“The study of relationship between two variables is called correlation analysis”
“The study or measure of degree of linear relationship between an independent variable and dependent variable is called correlation.”
Correlation analysis deals with the association between two or more variables----------------Simpson and Kafka
If two or more quantities vary in sympathy, so that movement in one tend to be accompanied by corresponding movements in the other, then they are said to be correlated --------------------Conner
Correlation analysis attempts to determine the degree of relationship between variables-----------Ya-Lun Chou
Utility of Correlation
We can measure the degree of relationship between different variables.
Correlation is the foundation of regression analysis
Estimation of various factor in economics, business and trade
Types of Correlation
Positive and Negative Correlation:
I) Positive Correlation: If two variables X and Y moves in same direction i.e. if one rises, other rises too and vice versa, then it is called a positive correlation e. g. money and supply
X
Demand
Sunlight
Y
Price
Temperature
Independent Variable
Dpendent Variable
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I) Negative Correlation: If two variables X and Y move in opposite direction i.e. if one rises , other falls , and if one falls other rises , then it is called as negative correlation e.g. demand and price
Linear and Curvi-Linear Correlation:
I) Linear Correlation: If the ratio of change of two variables X and Y remains constant throughout , then they are said to be linearly correlated their relationship is best described by straight line.
II) Curvi-Linear Correlation: The amount of change in one variable does not bear a constant ratio to the amount of change in the other variable e.g. when every time X rises by 10%, then Y rises by 20%,sometimes by 10% and sometimes by 40% then non linear or Curvi-linear correlation exists between them.
Simple Partial and Multiple Correlation:
I) Simple Correlation: Relationship between Two variables
II) Partial Correlation: Among three or more variables, relationship of two variables are studied assuming other as constant
III) Multiple Correlation: Study the relationship among three or more variable.
0
10
20
30
40
0
2
4
6
8
10
12
Positive Correlation
0
5
10
15
20
25
30
0
2
4
6
8
10
12
Negative Correlation
0
10
20
30
40
50
60
0
2
4
6
8
10
12
Curvi-Linear Correlation
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Properties of Correlation
1. Limits of coefficient of Correlation: value of ‘r’ lies between –1 and +1 i.e.
This implies that ‘r’ can never be greater than 1 and also it can’t take the value less than – 1.
2. Not Affected by Change of Origin and Scale. If the origin is shifted or scale is changed i.e.
If X changed to X – 3 and Y changed to Y – 2.
Then the value of correlation coefficient ‘r’ will be the same as for X and Y.
3. Geometric Mean of Regression Coefficients:
√ .
4. It is a Pure Number: ‘r’ is pure number and is independent of the units of measurements. This means that even if two variables are expressed in two different units of measurements e.g. Production in Tons, and power consume is in KW, the value of correlation comes out with a pure number. Thus it does not require that the units of both the variables should be the same.
5. Coefficient of correlation is Symmetric i.e.
:
It means that either we compute the value of correlation coefficient between x and y or between y and x , the coefficient of correlation remains the same.
6. If X and Y are independent variables, then coefficient of correlation is zero but the converse is not necessarily true.
If X and Y are two independent variables then ( , ) , ( , ) ,
Thus if X and Y are independent they are not correlated.
On the contrary : if r=0, the X and Y may not necessarily be independent.
Let the two variables X and Y has a relation then values of Y for different values of X according to the relation, and so the data will given in below table :
X
-3
-2
-1
0
1
2
3
Y
9
4
1
0
1
4
9
XY
-27
-8
-1
0
1
8
27
Hence , ( , ) . . .
Thus , ( , ) .
From the above calculation it is found that although coefficient of correlation is zero, but X and Y are not independent. In fact the variables are related by a quadratic equation i.e. there is a quadratic relation (i.e. non linear relationship) between the variables. This property implies that ‘r’ is only a measure of the linear relationship between X and Y. If the relationship is non-linear, the computed value of ‘r’ is no longer a measure of the degree of relationship between the two variables.
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Degree of Correlation:
The degree of Correlation can be Known by Coefficient of Correlation (r). Various types of correlation are mentioned in below table
S.No.
Degree of Correlation
Coefficient of Correlation (r)
Positive
Negative
1
Perfect Correlation
+1
-1
2
High Degree of Correlation
+0.75 to +1
-0.75 to -1
3
Moderate Degree of Correlation
+0.25 to + 0.75
-0.25 to - 0.75
4
Low Degree of Correlation
0 to +0.25
0 to -0.25
5
Absence of Correlation
0
0
Correlation and Causation
In a small sample it is possible that two variables are highly correlated but in universe or in population, these variables are unlikely to be correlated. Such type of meaningless correlation called causation and it may be either the fluctuations of pure random sampling or due to the bias of investigator in selecting the sample. The below example makes the point clear
Income (in Rs.)
5000
6000
7000
8000
9000
Weight (in Kg)
100
120
140
160
180
The above data stated, there is perfect positive correlation between monthly income and weight. Weight increases with rise in income. Even this kind of correlation can not be meaningful. Such relation is said to be spurious or non – sense correlation.
Another example of such type of correlation
No. of death cases and No. of manglik and non manglik couple
Manglik and Non Manglik Couple
200
300
400
500
600
700
Death Cases
2
3
4
5
6
7
The above data shows a perfect positive correlation between the no. of Manglik and Non – Manglik Couple and death cases in such type of couples. But this type of data has not any ground reality, this type of correlation in the data is called stupid correlation.