...Factor Analysis Assignment 1. The principal component analysis is the approach that is used for data reduction and creation of one or more than one index variables from the large number of variables. This happens with the use of linear combination of variables. The index variable that is created from this analysis is called components. While, the Factor Analysis is the approach that is used for data reduction in different way than principal component analysis. It is the measurement model of latent variable. This cannot be measured directly with one variable rather, it is observed through the relationship between x and y variables. 2. The general approach (Kaiser) is to retain factors with eigenvalue ≥ 1 and eliminate factors with eigenvalue...
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...Bhavsar2 1.Department of Statistics, S.V. Vanijya Mahavidyalaya, Ahmedabad, Gujarat, India 2.Department of Statistics, Gujarat University, Ahmedabad, Gujarat, India Email of the corresponding Author: m_a_shah73@yahoo.com Abstract We use two and half year data set of 50 companies of Nifty along with Nifty from 1st Jan 2009 to 28th June 2011 and apply multivariate technique for data reduction, namely Factor Analysis. Using Factor analysis we reduce these 50 companies’ data (50 variables) into the most significant 4 FACTORS. These four significant factors are then used to predict the Nifty using Multiple linear regression. We observed that the model is good fitted and it explained 90 % of the total variance. Keywords: Nifty, Factor Analysis, Multiple Linear Regression, Data reduction 1. Introduction: In this paper, we applying data reduction technique of Factor analysis on the Nifty Stocksand then predict NIFTY using Multiple Linear Regression Technique. Factor analysis is a statistical technique to study interrelationship among the Variables. The idea behind factor analysis is grouping the variables by their correlation in such a way that particular group is highly correlated among themselves but relatively smaller correlation with the variables in other group, and in such each group constructs a factor. The aim is to identify the unobservable Factor(latent) that simultaneously affects all the variables and try to understand the factor so that the change in variables can...
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...Introduction Simple linear regression is a model with a single regressor x that has a relationship with a response y that is a straight line. This simple linear regression model is y = β0 + β1x + ε where the intercept β0 and the slope β1 are unknown constants and ε is a random error component. Testing Significance of Regression: H0: β1 = 0, H1 : β1 ≠ 0 The hypotheses relate to the significance of regression. Failing to reject H0: β1 = 0 implies that there is no linear relationship between x and y. On the other hand, if H0: β1 = 0 is rejected, it implies that x is of value in explaining the variability in y. The following equation is the Fundamental analysis-of-variance identity for a regression model. SST = SSR + SSRes Analysis of variance (ANOVA) is a collection of statistical models used in order to analyze the differences between group means and their associated procedures (such as "variation" among and between groups), developed by R. A. Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. P value or calculated probability is the estimated probability of rejecting the null hypothesis (H0) of a study question when that hypothesis is true. VIF (the variance inflation factor) for each term in the model measures the combined effect of the dependences among the regressors on the variance of the term. Practical experience indicates that if any of...
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...Time Series Analysis Summary Tokelo Khalema 2008060978 BSc. Actuarial Science University of the Free State Bloemfontein November 1, 2012 Time Series Analysis A time-series is a stochastic process {Xt : t = 1, . . . , T } with a continous state space and discrete time domain. It arises naturally as an ordered series of values observed over time. Examples include daily closing prices of a stock index recorded over several years, say, the flow rate of the River Nile, road casualties in Great Britain over the years 1969-84, etc. Stationary time-series are particularly easy to analyse. A series is stationary if its mean and variance are constant over time. Special aids are available to help determine whether or not a series is stationary. Particularly notable in this regard are the autocorrelation function (ACF) and the partial autocorrelation function (PACF). These are plots of the sample autocorrelation and partial autocorrelation coefficients at various time lags, respectively. If the ACF decays gradually to zero, then the series is non-stationary. If on the other hand the ACF and PACF decay rapidly to zero, then the series is stationary. A series being non-stationary can be brought about by, among others, a trend, irregular fluctuations, or seasonal variation. Non-constant variance, or as commonly called, heteroscedasticity can be eliminated by using a variance-stabilising transformation. A number of ways exist that eliminate a trend. Two of which are, to subtract a regression line...
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...Comparative Analysis of the Impact of Macro-economic Variables on the GDP of China and India by Manish Chandi Shrestha Submitted to the Program of Analytics in the Postgraduate Division of the Business School As part of the requirement for Master of Business Administration at Bournemouth University March, 2015 Contents List of acronyms i List of figures and tables ii Abstract 1 Introduction 1 Methodology 2 Data source 3 Findings 3 Interpretation 4 Conclusion 9 References 10 Appendices 11 List of Acronyms GDP Gross Domestic Product IMF International Monetary Fund IQR Inter Quartile Range ANOVA Analysis of Variance BLUE Best Linear Unbiased Estimator VIF Variance Inflation Factor List of Figures and Tables 1. Correlation Analysis of China 4 2. Correlation Analysis of India 4 3. Beta coefficients for China and India 5 4. Revised Beta Coefficients for China 5 5. Comparison between Predicted and Actual GDP for China 6 6. Comparison between Predicted and Actual GDP for India 7 7. Test of Normality of Error for China and India 7 8. Residual Statistics for India 8 9. Residual Statistics for China 8 10. Collinearity Statistics for India...
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...Bus. 463 Project Report, Extended Geo Mean, Jensen-Alpha Measure April 1st, 2013 Table of Contents Client Description……………………………………………………………………………………3 Discussion of Models……………………………………………………………………………...4 Markowitz Model………………………………………………………………………..4-5 Single-Index Model………………………………………………………………………..5 Geometric Mean…………………………………………………………………………….6 Recommendations…………………………………………………………………………………6-7 Analysis……………………………………………………………………………………………………7 Appendix A………………………………………………………………………………………………8 References……………………………………………………………………………………………….9 Client Description Joe Schedin is 45-years-old, who has spent the last 18 years working for Costco as a meat cutter. He will be switching jobs as he wants to do something new and more exciting so he will be able to contribute $110,000 to add to the current portfolio. He wants to be able to retire in 20 years, by age 65, and would like to have at least a million dollars for retirement as well as a surplus of greater than or at least $40,000 in order to pay for his new step-son’s college fund. He would like to be able to only use about half of the retirement to live off of, and keep the rest either invested in his portfolio, or set up college funds, IRA’s, etc. to help his family with his grandchildren and give them a chance for a higher education. With this information I was able to calculate a yearly rate of return needed to generate at least $1.1 million dollars with the initial investment of $152,212, compounded over...
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...1. Introduction: We know the fact that low interest rate affects stock market price. Low interest rate decreases the cost of capital and increases the confidence of investors. The equity risk premium is the "extra return" that investors collectively demand for investing their money in stocks instead of holding it in a risk less or close to risk less investment. As a consequence, equity risk premium reflects both investor hopes and fears about stocks, rising as the fear factor increases. As a measure the equity risk premium can be an individual stock or the overall stock market provides over a risk-free rate. And the size of the premium will be a standard to compensate with a higher premium in the stock market. Thus, a portfolio manager when the equity risk premium increases in the future, the investors will sell out stock market because the stocks are over priced. So the legislators and pension administrators decide how much to set aside to meet future pension obligations, based upon assessments of equity risk premiums. However the history data of ERP (Equity Risk Premium) from Federal Reserve System shows it keeps low and stable state but increases suddenly since 2006. At the same time the Federal Funds Effective Rate goes down and keeps low state. We know that interest rate is a way to control inflation. Inflation is a factor causes too much money chasing too few goods. “Changes in the federal funds rate affect the behavior of consumers and businesses...
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...Chapter 14 Factor analysis 14.1 INTRODUCTION Factor analysis is a method for investigating whether a number of variables of interest Y1 , Y2 , : : :, Yl, are linearly related to a smaller number of unobservable factors F1, F2, : : :, Fk . The fact that the factors are not observable disquali¯es regression and other methods previously examined. We shall see, however, that under certain conditions the hypothesized factor model has certain implications, and these implications in turn can be tested against the observations. Exactly what these conditions and implications are, and how the model can be tested, must be explained with some care. 14.2 AN EXAMPLE Factor analysis is best explained in the context of a simple example. Students entering a certain MBA program must take three required courses in ¯nance, marketing and business policy. Let Y1, Y2 , and Y3 , respectively, represent a student's grades in these courses. The available data consist of the grades of ¯ve students (in a 10-point numerical scale above the passing mark), as shown in Table 14.1. Table 14.1 Student grades Student no. 1 2 3 4 5 Finance, Y1 3 7 10 3 10 Grade in: Marketing, Y2 6 3 9 9 6 Policy, Y3 5 3 8 7 5 °Peter Tryfos, 1997. This version printed: 14-3-2001. c 2 Chapter 14: Factor analysis It has been suggested that these grades are functions of two underlying factors, F1 and F2, tentatively and rather loosely described as quantitative ability and verbal ability, respectively. It is...
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...it is recommended that the leadership of Competition Bikes, Inc, (CBI) consider all options presented to optimize future corporate growth. The CEO of Competition Bikes, Inc. requested a review of current budgetary information (“Year 8”) projection for the upcoming business year. Areas of analysis and management intervention have been reviewed based on data provided by CBI. Competition Bikes, Inc.’s “Year 9” budget (pro forma) has been based on financial information provided based on a current trend analysis from three previous years and focusing on “Year 8” financials. A master budget was created to plan and control revenues and costs for future growth and corporate development for “Year 9.” The benefit to CBI leadership in reviewing “Year 9” financial plans allows for decision-making on planning, coordination of operations, and benchmarking for an evaluation of actual performance at the end of “Year 9.” To review, a static budget does not change after it is developed, however, a flexible budget is one that summarizes revenues and costs from different volumes compared to similar ranges to like companies. Since a flexible budget is more complex and difficult to predict due to variances in costs compared to a fixed budget, it is necessary to answer questions when selling items with...
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... Friday, April 16th, 2010 TABLE OF CONTENTS I. Introduction: Marketing Research 4 1) Marketing Research 4 2) The Marketing Research process 4 II- Body 1: Litterature Review 6 1) Inferential Statistics 6 a) Dummy Variables 7 b) Experimental Analysis 7 2) Normal Distribution 8 Figure 1: A normal Distribution, bell-shaped curve 9 3) Skewness 9 4) The Kurtosis 9 5) Formula of Kurtosis and Skewness over their Standard error 10 6) Central Limit Theorem 10 7) T Test Hypothesis testing for one sample mean 11 a) State the Null and Alternative Hypothesis 11 b) Hypothesis of the Testing 11 c )Choosing the Level of Significance 12 d) Calculate the test statistic for One Sample Mean 13 8) Independent Samples t-Test 13 a) Stating the Null and Alternative Hypothesis 14 b) Assumptions of the Testing 14 c) Choosing the Level of Significance 15 d) Calculate the test statistic for independent samples 15 e) Interpreting the Results 16 9) Risks in Decision Making Using Hypothesis Testing 17 10) The β Risk 17 III- Body II: Application 1: One Sample Testing 18 1) The Research Topic 18 2) Decriptives for the Students Sample 18 a) Range, Mean, Standard Deviation 18 b) Variance, Skewness, Kurtosis 19 c) Histogram of the Student Sample 19 3) Hypothesis of the independent sample t test 20 4) T test for the sample mean 20 a) State the Null and Alternative Hypothesis 20 b) Selection of the significant level 21 c) SPSS Output 22 d) Conclusion...
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...AMR Project Section B Group 6 AMR PROJECT SYNOPSIS TOPIC:”Consumer purchase behavior in out-ofstock situations at retail outlets” Submitted by : Group 6 Section B Page 1 AMR Project Section B Group 6 PROBLEM STATEMENT/PURPOSE Model the consumer purchase behaviour in out of stock situations in retail outlets RATIONALE OF CHOOSING THE PROBLEM STATEMENT Out of stock situations in retail outlets trigger customer behaviour like switching to other brands, stores, items, postponing or cancelling purchases etc. This hampers customer loyalty and leads to lost sales for retailers. Hence, it is important for retailers to know the possible consumer behaviours in stock out situations. The magnitude of stock-out sales losses, as well as whether they primarily affect the Manufacturer or the Retailer, strongly varies with the way consumers react. Assuming the margins to the retailer on the considered brands are same, if consumers buy another brand in the same store, this is detrimental to the manufacturer not the retailer. Conversely, if consumers look for the missing item elsewhere, the retailer incurs a loss. Manufacturers and retailers must, therefore, anticipate the specific type of OOS responses. MANAGEMENT DECISION PROBLEM How can customer retention be increased during stock out situations in a retail store? An area of concern for many retailers is the availability of various brands at retail level. Of most concerns to retailers is the possibility...
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...Sharrain Walls Variance Analysis Grand Canyon University: HCA-530 July 5, 2016 Introduction Various reports help with viewing and keeping track of the productivity of a department. Managers find these reports very helpful with assisting to find an issue, trend, overspending, and underspending. A report commonly used is a variance report, which compares the planned amount to the actual amount. This report is critical in determining major decisions and viewing fluctuations. The report can be in the form of a table or graph and can be considered favorable or unfavorable based on the results. Vice Presidents look for the report to be clear and direct. Managers should include all factors associated with the variance report as well as the relationships between variance reporting, interpreting variance report results, and actual reports. Variance Analysis When viewing the results of the report consider the hospital size and utilization of the services offered by the hospital. When performing a variance analysis, relationships can be identified. Favorable (positive) and unfavorable (negative) correlations are critical in business planning. An example would be, variance analysis may show that when sales for product a rise in sales for product B. This type of relationship may be used for success of other products (Cross, N.d.). When using a variance report for forecasting variance data allows managers to identify factors such as seasonal changes for the favorable and unfavorable...
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...Chapter 8 © 2008 McGraw-Hill Ryerson Limited. Standard Costs Predetermined. Standard Costs are Used for planning labour, material and overhead requirements. Benchmarks for measuring performance. Used to simplify the accounting system. © 2008 McGraw-Hill Ryerson Limited. Standard Costs Managers focus on quantities and costs that exceed standards, a practice known as management by exception. Amount Standard Direct Material Direct Labour Manufacturing Overhead Type of Product Cost © 2008 McGraw-Hill Ryerson Limited. Setting Standard Costs Accountants, engineers, personnel administrators, and production managers combine efforts to set standards based on experience and expectations. © 2008 McGraw-Hill Ryerson Limited. Setting Standard Costs Should we use practical standards or ideal standards? Engineer Managerial Accountant © 2008 McGraw-Hill Ryerson Limited. Setting Standard Costs Practical standards should be set at levels that are currently attainable with reasonable and efficient effort. Production manager © 2008 McGraw-Hill Ryerson Limited. Setting Standard Costs I agree. Ideal standards, which are based on perfection, are unattainable and discourage most employees. Human Resources Manager © 2008 McGraw-Hill Ryerson Limited. Note • The argument that ideal standards are discouraging has been persuasive for many years. So “normal” defects and waste were built into the standards. • In recent years...
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...return distributions. Even within a single asset class the return distributions of assets are not alike. We assume that the return distributions of all risky assets are known and would like to choose the best asset to invest to, meaning that the risky assets are mutually exclusive investment alternatives. How to do this? The standard approach in financial theory and practice is to employ some portfolio performance measure to rank the various risky investments. Each portfolio performance measure calculates a score for each asset using its probability distribution of returns. The best asset to invest to is the asset with the highest score. The Sharpe ratio is a commonly used measure of portfolio performance. But because it is based on mean-variance theory, this measure can only be used in some restrictive cases, for example, when return distributions are normal. When return distributions are non-normal, the Sharpe ration can lead to misleading conclusions and unsatisfactory paradoxes, see Bernardo and Ledoit (2000) and Hodges (1998). There have been proposed numerous universal performance measures that, in one way or the other, are alternatives to the Sharpe ratio and try to take into account non-normality of return distributions. For some examples, see Sortino and Price (1994), Dowd (2000), Stutzer (2000), Keating and Shadwick (2002), Gregoriou and Gueyie (2003), Kaplan and Knowles (2004), and Ziemba (2005). The main drawback of many of these alternative performance measures is that...
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...Chapter 6: Efficient Diversification General thought: Risk comes from different places. Some risk comes from common sources, like the economy. Other risk comes from sources unique to each asset. This means that some kinds of risk can be diversified. Return and Risk for a Portfolio 0 First, need to know how much you’ve invested in each asset (w) as a percentage of your total funds invested. Expected return on a portfolio In other words, portfolio expected return is always a weighted average of the expected returns of the assets within the portfolio. However, this is not true of portfolio standard deviation! * Portfolio standard deviation depends on covariance / correlation between each pair of assets within the portfolio…how much the movements between each pair of assets offset each other. * In general, portfolio standard deviation will be less than the weighted average of the standard deviations of the individual assets within the portfolio. 1 Covariance =: Tells you how much any pair (two) stocks (i and j) move around together: | Prob. | 1 | 2 | Great | .3 | .2 | .1 | OK | .5 | .1 | .2 | Bad | .2 | - .05 | .4 | = -.0033 + 0 + -.0057 = -.009 Correlation between Two Assets The correlation coefficient “standardizes” covariance – puts it into a form that tells you how much two assets actually move together. Correlation coefficients are scaled between –1 and +1: = = -.995 Finally, we can...
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