...Introduction to Multiple Regression Dale E. Berger Claremont Graduate University http://wise.cgu.edu Overview Multiple regression is a flexible method of data analysis that may be appropriate whenever a quantitative variable (the dependent or criterion variable) is to be examined in relationship to any other factors (expressed as independent or predictor variables). Relationships may be nonlinear, independent variables may be quantitative or qualitative, and one can examine the effects of a single variable or multiple variables with or without the effects of other variables taken into account (Cohen, Cohen, West, & Aiken, 2003). Multiple Regression Models and Significance Tests Many practical questions involve the relationship between a dependent or criterion variable of interest (call it Y) and a set of k independent variables or potential predictor variables (call them X1, X2, X3,..., Xk), where the scores on all variables are measured for N cases. For example, you might be interested in predicting performance on a job (Y) using information on years of experience (X1), performance in a training program (X2), and performance on an aptitude test (X3). A multiple regression equation for predicting Y can be expressed a follows: (1) [pic] To apply the equation, each Xj score for an individual case is multiplied by the corresponding Bj value, the products are added together, and the constant A is added to the...
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...MULTIPLE REGRESSION After completing this chapter, you should be able to: understand model building using multiple regression analysis apply multiple regression analysis to business decision-making situations analyze and interpret the computer output for a multiple regression model test the significance of the independent variables in a multiple regression model use variable transformations to model nonlinear relationships recognize potential problems in multiple regression analysis and take the steps to correct the problems. incorporate qualitative variables into the regression model by using dummy variables. Multiple Regression Assumptions The errors are normally distributed The mean of the errors is zero Errors have a constant variance The model errors are independent Model Specification Decide what you want to do and select the dependent variable Determine the potential independent variables for your model Gather sample data (observations) for all variables The Correlation Matrix Correlation between the dependent variable and selected independent variables can be found using Excel: Tools / Data Analysis… / Correlation Can check for statistical significance of correlation with a t test Example A distributor of frozen desert pies wants to evaluate factors thought to influence demand Dependent variable: Pie sales (units per week) ...
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...In multiple linear regression analysis, R2 is a measure of the ________. A) homoskedasticity of the predictors B) misclassification rate C) percentage of the variance of the dependent variable that is explained by the set of independent (predictor) variables D) precision of the resulting model when applied to the validation data 2. Categorical variables can be used in a multiple linear regression model _________. A) by partitioning of the dataset B) when no multicollinearity among the independent variables is present C) when the sample size is at least 10 times that of the number of variables D) through the use of dummy variables 3. In multiple linear regression analysis “multicollinearity” refers to _________. A) two or more predictors sharing the same linear relationship with the outcome variable B) a high degree of correlation between the dependent variables C) the equality of the variance of the dependent throughout its range of values D) None of the above. 4. In multiple regression analysis, which of the following is an example of a subset selection algorithm? A) Forward selection B) Backwards elimination C) Stepwise regression D) All of the above 5. _________ is an important property of a good model. A) Complexity B) Independence C) Parsimony D) None of the bove 6. An assumption that applies to the linear multiple regression method is that the distribution of the error term values should be ________. A) standardized ...
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...Benckiser A Report on “Multiple Regression Analysis of Determinants of Dividend Payout Ratio of Reckitt Benckiser” Acknowledgement It is a great honor for us to submit this report to our respected teacher. At first we want to convey our thanks and gratitude to her for assigning us to prepare report entitled, “Reckitt Benckiser”. It would not have been possible for us to complete the report, but for his help. All of the efforts ended at a desired point for the cooperation and hard work, Sincerity and seriousness of our group members. So, all of them as well as our group members are worth of pure compliment. Letter of Transmittal February 14, 2015 Dear Sir, Subject: Submitting the report on “Determinants of dividend payout ratio of Reckitt Benckiser”. We are submitting a well-structured and comprehensive report on Reckitt Benckiser”. Despite many constraints like scope and access to information, we have tried to create something satisfactory. We have tried to follow your guideline in every aspects of preparing this report. We have concentrated on the most relevant and logical areas to make our report coherent as well as practical. We hope this report will entice your kind appreciation. Sincerely, ________________ Executive Summery Reckitt Benckiser is a global leader in household, health and personal care sectors and one of the fast growing multinationals. In our report we mainly deal with Multiple regression analysis of determinants...
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...Journal of Data Science 2(2004), 329-346 Estimating Optimal Transformations for Multiple Regression Using the ACE Algorithm Duolao Wang1 and Michael Murphy2 School of Hygiene and Tropical Medicine and 2 London School of Economics 1 London Abstract: This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (1985) for estimating the transformations of a response and a set of predictor variables in multiple regression that produce the maximum linear effect between the (transformed) independent variables and the (transformed) response variable. These transformations can give the data analyst insight into the relationships between these variables so that relationship between them can be best described and non-linear relationships can be uncovered. The power and usefulness of ACE guided transformation in multivariate analysis are illustrated using a simulated data set as well as a real data set. The results from these examples clearly demonstrate that ACE is able to identify the correct functional forms, to reveal more accurate relationships, and to improve the model fit considerably compared to the conventional linear model. Key words: Alternating conditional expectation (ACE) algorithm, nonparametric regression, transformation. 1. Introduction In regression analysis, we try to explain the effect of one or more independent variables (predictors or covariates) on a dependent variable (response). The initial stages of data analysis...
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...Forecasting Gold Prices Using Multiple Linear Regression Method Z. Ismail, 2A. Yahya and 1A. Shabri Department of Mathematics, Faculty of Science 2 Department of Basic Education, Faculty of Education University Technology Malaysia, 81310 Skudai, Johor Malaysia 1 1 Abstract: Problem statement: Forecasting is a function in management to assist decision making. It is also described as the process of estimation in unknown future situations. In a more general term it is commonly known as prediction which refers to estimation of time series or longitudinal type data. Gold is a precious yellow commodity once used as money. It was made illegal in USA 41 years ago, but is now once again accepted as a potential currency. The demand for this commodity is on the rise. Approach: Objective of this study was to develop a forecasting model for predicting gold prices based on economic factors such as inflation, currency price movements and others. Following the melt-down of US dollars, investors are putting their money into gold because gold plays an important role as a stabilizing influence for investment portfolios. Due to the increase in demand for gold in Malaysian and other parts of the world, it is necessary to develop a model that reflects the structure and pattern of gold market and forecast movement of gold price. The most appropriate approach to the understanding of gold prices is the Multiple Linear Regression (MLR) model. MLR is a study on the relationship between a single dependent...
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...------------------------------------------------- india Will Be The Great Power by 2035 Spiritually Economically Militarily.Indian Economy Will Have Slowdown in 2011 With its GDP Growth Reaching 8.0% .Great Scientific Discoveries will be made by Indians Throughout the world. It will become one of the Richest Countries of The world. India's Great Sanatana Dharma, Yoga, Spirituality, Popularity Will Soar Worldwide.Inflation & Interest Rates Will Continue to be High In 2011 in India & government of india will lie to its people by manipulating Statistics.Stock Markets Will Touch New Heights But will Decline in middle of 2011.Gold and Silver prices will also Rise.Crime Will Soar In India 2011, Prostitution & Drug Peddling and Mafia will flourish under the goverment protection. Primeminister will be weak and goverment dishonest & shameless. Despite a recession at the beginning of the century, developing countries have posted healthy economic growth rates over the last 15 years. These growth rates were maintained despite the ageing of the population in the developed world by harnessing energies of younger people in developing economies. The economic prosperity has also resulted in the global tourism industry registering strong growth. Realising the potential size of the opportunity in 2002, India put in place initiatives to tap it despite the uncertainty associated with the future. As part of its plan, India Inc. positioned its brand as a credible and value-for-money...
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...Ego Defence Mechanisms Introduction Ego psychology embodies a more optimistic and growth oriented view of human functioning and potential than do the earlier theoretical formulation. It generated changes in the study and assessment process and led to an expansion and systemization Of interceptive strategies with individuals. It fostered a re-conceptualization of the clinic worker relation ship, of change mechanisms, and of the interventive process. It helped to refocus the importance of wok of with the social environment as well as work with the family and the group. Moreover, it has important implications for the design of service delivery, large-scale social programs, and social policy. DEFINITION OF DEFENCE MECHANISM Ego-defense mechanisms are learned, usually during early childhood and are considered to be maladaptive when they become the predominant means of coping with stressors. What is EGO psychology? Ego psychology comprises a related set of theoretical concepts about human behavior that focus on the origins, development, structure, and functioning of the executive arm of the personality _the ego_ and its relationship to other aspects of the personality and to the external environment. The ego is considered to be a mental structure of the personality responsible for negotiating between the internal needs of the individual and the outside world. The following seven propositions characterize ego psychology’s view of human...
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...University of Phoenix Material Week 4 Review Worksheet Psychodynamic Theories Complete the following table. |Theorists |Main tenets of theory |Unique contributions |Limitations | |Freud | | | | | | | | | | | | | | | | | | | |Jung | | | | | | | | | | | | | | | | | | | |Adler | | |...
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...Repression occurs when a person unconsciously holds back unwanted or stressful emotions to protect themselves from reliving or acknowledging an experience. A subject can repress certain thoughts in whole or partially depending on the extent of the trauma. While attending this class I have realized that since my early teens, I have been repressing emotions that stem from sexual abuse by a person who was both a family friend and our church pastor. This realization was brought to the forefront because my wife and children enjoy attending church services and participating in church related activities, while I will make up excuses to not attend. My lack of attendance at church is a frequent subject in our household and the cause of more than a few heated discussions. The thought of going to a church service makes me uneasy and I do it only after much prodding from my wife, but even then I only go for a couple of weeks before I start making excuses again. It was after one of these discussions that I decided to use the things I had read and try to understand why I don’t like going to church. That’s when I recognized the correlation between the abuse and my lack of interest in church. Now that I recognize my apprehension toward going to church services is because I’m trying to avoid the emotions from the abuse I am going to re-evaluate my views on attending church services. Who knows, maybe I’ll like going and that will make my wife happy and relieve some stress between us. I’m not...
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...Mechanism Denial: when my grandfather passed away, I was told about it while I was still in university and after hearing it I went back to the lounge and laughed with my friends as if nothing happened. Projection: I’ve been wanting to eat healthy and stop eating junk food but I still do eat junk food and every time I see my brother having junk food I lecture him about how unhealthy and bad it, same thing happens when he asks for it. Repression: once my parents were having a fight and I just put my head phones on and started watching a movie as if nothing was happening and to this day I remember doing it but not to the extent that my sister remembers it. She says that my parents almost had a divorce but I remember it as a normal fight. Regression: when my younger brother was born. I started wanting to drink from the bottle again and sleep next to my parents. Reaction Formation: In school a lot of my classmates were super religious and had a strong opinion on praying like a person should force themselves to pray so they can be good Muslims but I don’t agree with that, I do miss prayers because I feel like a person should want to pray and it’s more than just getting the “job” done but I never said anything and would agree with them. Displacement: once before a wedding I didn’t like the way I did my hair and when my sister came to help me with my makeup I started screaming at her and telling her she’s doing things wrongly and it was because of her I didn’t want to go to the...
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...the exam. Material preparation refers to the physical items to be taken for the exam. Physical preparation refers to specific care about food, sleep and rest. Mental preparation refers to the attitude and self responsibility, avoidance of tension and stress and being motivated and charged to take up the exam. Substantive Preparation for examinations: 1. What to read?: There is so much to read on any subject like textbooks, study guides, reference books, suggested answers etc. Read all text books and prescribed reading. 2. How to read? How to read addresses issues of methodology of reading and various reading practices. One technique is that of faster reading by not reading word-to-word and not going for re-reading called regression. Faster reading saves a lot of time. Amongst many techniques aimed at better reading, SQ3R is one of the most powerful techniques. This technique is very effectively used by me from 12th standard to Chartered Accountant, IIM MBA and CFA course. This technique is the basic foundation of my academic success leading to consistent rank holding career and I would very strongly recommend to all students. The full form of SQ3R is survey, question, read, recite and review. Let me explain this technique in brief as under: a) Survey: Survey the reading material before you actually start the reading. Here you are doing study of the title, main sections, going through preface to the subject and thereby creating your mental framework as to what...
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...Statistical Project Assignment | Statistics for Business & Economics | | DATASET 1: SIMPLE REGRESSION ANALYSIS Variable Definition Xi = Weight of car (pounds) Yi = Price of car ($) 1. (a) Regression Model using X to predict Y Weight and Price of Car Sales | | | | | | | | | | | | | Regression Statistics | | | | | | Multiple R | 0.212585295 | | | | | | R Square | 0.045192508 | | | | | | Adjusted R Square | 0.038951936 | | | | | | Standard Error | 7883.368653 | | | | | | Observations | 155 | | | | | | | | | | | | | ANOVA | | | | | | | | df | SS | MS | F | Significance F | | Regression | 1 | 450055137.6 | 450055137.6 | 7.241725381 | 0.007915154 | | Residual | 153 | 9508567701 | 62147501.31 | | | | Total | 154 | 9958622839 | | | | | | | | | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Intercept | 9854.041192 | 2894.819474 | 3.404026151 | 0.000847889 | 4135.063875 | 15573.01851 | Weight | 2.843766419 | 1.056751555 | 2.691045407 | 0.007915154 | 0.756058281 | 4.931474557 | Table 1 – Simple Linear Regression Model (Y and X) Simple linear regression equation Ŷi=b0+b1Xi From Table 1, we can see that b0 = 9854.0412 and b1 = 2.8438 Ŷi=9854.0412+2.8438Xi Figure 1 – Scatter Plot – Weight of Car vs Price of Car (b) Interpret the slope b1 measures the estimated change in the average value of Y as a result of...
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...are countless more you could use. High low method for revenue Ton Miles (High-2,369, low-1,580) by Salary Cost(High-1,607, Low1,037) :(2,369-1,580)/(1,607-1,037)= 789/570=1.384 I selected this driver because the revenue directly correlates to the price you could pay your employees and still turn a profit. Delta can use this to see that they are making a profit when looking at just the salary cost and the revenue they bring in. The advantages of this technique are you have concrete evidence when and if employees ask how much they are getting paid and why and the disadvantages are that the revenue Ton Miles can fluctuate over the course of a year and make it hard to base the decision of salaries on just one variable. 2.Use simple regression to estimate the salary cost function for Delta Airlines. Comment on the statistical validity and significance of your results. What are the advantages of this technique? What are the disadvantages? Is this technique an improvement from the High-Low Method? Revenue Ton Miles and Salary Cost, Y=.3301X+614.33 with its R^2=.1378 This was not the best variable to use considering that the R square for the “Available Ton Mile” is much smaller equaling .5577 this means that the correlation...
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...s 11-17-09 OIS 3440 Capstone Project Executive Summary My goal was to gather finance information and establish relationships between eight different variables. I incorporated the following variables into a small survey: Age, Income, Investment, Number of Children, Number of Years of college, Additional Investment for the Current Year and Home Value. The reason for studying this data is because I am a finance major and going to be working towards becoming a financial advisor. I created a survey that answered the questions for the criteria listed above. I asked friends and family through email and facebook, and told them the reason for my asking. Everyone was willing to participate, as I kept their personal information confidential. I took the survey results and computed with 49 surveys. After analyzing the data I noticed that there were many relationships amongst the variables. Based on the research I concluded that the higher the age the more that they are willing to invest for the current year. There was also a strong relationship between age and income. The older the person, the more money they made. The dependent variable was age. Older people make more money, are more familiar with investments, and are more willing to make larger investments currently. Also, age related to home value in that an increase in age was related to an increase in home value. Analysis Investments | Income | Education | Kids | Home Value | Additional Investments | Age | ...
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