Submitted By sandyda04

Words 1282

Pages 6

Words 1282

Pages 6

Student Name

Grantham University

BA/520 – Quantitative Analysis

Instructor Name

April 6, 2013

Abstract

This paper will refer to regression models and the benefits that variables provide when developing and examining such models. Also, it will discuss the reason why scatter diagrams are used and will describe the simple linear regression model and will refer to multiple regression analysis as well as the potential uses for this type of model.

Regression Models Regression models are a statistical measure that attempts to determine the strength of the relationship between one dependent variable (usually denoted by Y) and a series of other changing variables (known as independent variables). Regression models provide the scientist with a powerful tool, allowing predictions about past, present, or future events to be made with information about past or present events. Inference based on such models is known as regression analysis. The main purpose of regression analysis is to predict the value of a dependent or response variable based on values of the independent or explanatory variables. According to Render, Stair, and Hanna (2011) they are two reasons for which regression analyses are used: one is to understand the relation between various variables and the second is to predict the variable's value based on the value of the other. Variables provide many advantages when creating models. One of the advantages is that the model can be shaped in various ways which would offer the possibility of analysis from different perspectives. The two basic types of regression are linear regression and multiple regressions. Linear regression uses one independent variable to explain and/or predict the outcome of Y, while multiple regressions use two or more independent variables to predict the outcome.…...

...Regression Analysis: Basic Concepts Allin Cottrell∗ 1 The simple linear model Suppose we reckon that some variable of interest, y, is ‘driven by’ some other variable x. We then call y the dependent variable and x the independent variable. In addition, suppose that the relationship between y and x is basically linear, but is inexact: besides its determination by x, y has a random component, u, which we call the ‘disturbance’ or ‘error’. Let i index the observations on the data pairs (x, y). The simple linear model formalizes the ideas just stated: yi = β0 + β1 xi + ui The parameters β0 and β1 represent the y-intercept and the slope of the relationship, respectively. In order to work with this model we need to make some assumptions about the behavior of the error term. For now we’ll assume three things: E(ui ) = 0 2 2 E(ui ) = σu E(ui u j ) = 0, i = j u has a mean of zero for all i it has the same variance for all i no correlation across observations We’ll see later how to check whether these assumptions are met, and also what resources we have for dealing with a situation where they’re not met. We have just made a bunch of assumptions about what is ‘really going on’ between y and x, but we’d like to put numbers on the parameters βo and β1 . Well, suppose we’re able to gather a sample of data on x and y. The task ˆ of estimation is then to come up with coefﬁcients—numbers that we can calculate from the data, call them β0 and ˆ1 —which serve as estimates of the unknown......

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...Q1: All the regressions were performed. Output can be made available if needed. See outputs for Q2 in appendix. Q2: Select the model you are going to keep for each brand and explain WHY. Report the corresponding output in an appendix attached to your report (hence, 1 output per brand) We use Adjusted R Squared to compare the Linear or Semilog Regression. R^2 is a statistic that will give some information about the goodness of fit of a model. In regression, the Adjusted R^2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data. Brand1: Linear Regression R^2 | 0.594 | SemiLog Regression R^2 | 0.563 | We use the Linear Regression Model since R-squared is higher. Brand 2: Linear Regression R^2 | 0.758 | SemiLog Regression R^2 | 0.588 | We use the Linear Regression Model since R-squared is higher Brand 3: Linear Regression R^2 | 0.352 | SemiLog Regression R^2 | 0.571 | We use the Semilog Regression Model since R-squared is higher Brand 4: Linear Regression R^2 | 0.864 | SemiLog Regression R^2 | 0.603 | We use the Linear Regression Model since R-squared is higher Q3: Here we compute the cross-price elasticity. Depending on whether we use linear or semi-log model, Linear Model Linear Model Semi-Log Model Semi-Log Model ` ...

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...relationships between the variables. The relationships can either be negative or positive. This is told by whether the graph increases or decreases. Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.069642247 R Square 0.004850043 Adjusted R Square -0.00471871 Standard Error 0.893876875 Observations 106 ANOVA df SS MS F Significance F Regression 1 0.404991362 0.404991 0.50686 0.478094147 Residual 104 83.09765015 0.799016 Total 105 83.50264151 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.506191723 0.363736853 15.13784 4.8E-28 4.784887893 6.2274956 4.7848879 6.22749555 Benefits -0.05716561 0.080295211 -0.711943 0.47809 -0.21639402 0.1020628 -0.216394 0.10206281 Y=5.5062+-0.0572x Graph Benefits and Extrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.161906 R Square 0.026214 Adjusted R Square 0.01685 Standard Error 1.001305 Observations 106 ANOVA df SS MS F Significance F Regression 1 2.806919 2.806919 2.799606 0.097293 Residual 104 104.2717 1.002612 Total 105 107.0786 Coefficients Standard Error t Stat P-value Lower 95% Upper......

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...Linear Regression deals with the numerical measures to express the relationship between two variables. Relationships between variables can either be strong or weak or even direct or inverse. A few examples may be the amount McDonald’s spends on advertising per month and the amount of total sales in a month. Additionally the amount of study time one puts toward this statistics in comparison to the grades they receive may be analyzed using the regression method. The formal definition of Regression Analysis is the equation that allows one to estimate the value of one variable based on the value of another. Key objectives in performing a regression analysis include estimating the dependent variable Y based on a selected value of the independent variable X. To explain, Nike could possibly measurer how much they spend on celebrity endorsements and the affect it has on sales in a month. When measuring, the amount spent celebrity endorsements would be the independent X variable. Without the X variable, Y would be impossible to estimate. The general from of the regression equation is Y hat "=a + bX" where Y hat is the estimated value of the estimated value of the Y variable for a selected X value. a represents the Y-Intercept, therefore, it is the estimated value of Y when X=0. Furthermore, b is the slope of the line or the average change in Y hat for each change of one unit in the independent variable X. Finally, X is any value of the independent variable that is......

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...FOR ENGINEERS (EQT 373) TUTORIAL CHAPTER 3 – INTRODUCTORY LINEAR REGRESSION 1) Given 5 observations for two variables, x and y. | 3 | 12 | 6 | 20 | 14 | | 55 | 40 | 55 | 10 | 15 | a. Develop a scatter diagram for these data. b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c. Develop the estimated regression equation by computing the values and. d. Use the estimated regression equation to predict the value of y when x=10. e. Compute the coefficient of determination. Comment on the goodness of fit. f. Compute the sample correlation coefficient (r) and explain the result. 2) The Tenaga Elektik MN Company is studying the relationship between kilowatt-hours (thousands) used and the number of room in a private single-family residence. A random sample of 10 homes yielded the following. Number of rooms | Kilowatt-Hours (thousands) | 12 9 14 6 10 8 10 10 5 7 | 9 7 10 5 8 6 8 10 4 7 | a. Identify the independent and dependent variable. b. Compute the coefficient of correlation and explain. c. Compute the coefficient of determination and explain. d. Test whether there is a positive correlation between both variables. Use α=0.05. e. Determine the regression equation (used Least Square method) f. Determine the value of kilowatt-hours used if number of rooms is 11. g. Can you use the model in (f.) to predict the kilowatt-hours if number of rooms is 20?......

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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......

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...is more reliable. If it is the case that the cost of suicide to the society is very significant that we need to do some prevention, then once we get the idea of what the important determinants are, we can focus on the ones have most impact. For example, if the higher the education level is, the fewer people tend to commit suicide, we can try to subsidize education and improve the overall education level of people, and then we expect suicide rate will be lower according to this action. If we find out that the suicide rate for some specific age group is relatively higher than the other groups, we may set up some program providing help specifically to this group. This research will also be interesting, because we want to examine if the regression result is in compliance with our common sense (what effect on suicide rate there will be for each different variable). This will be discussed in more details in part B. Part B: Research design – motivation and estimation of independent / dependent variables Dependent Variable (Y) – Suicide rate This is just what we want to do research on, and the way it is calculated is as following: Independent Variable (X) Education impact (High school completion rate, and % of population get Bachelor’s degree or more), calculated as People with higher education tend to be better at adapting themselves to shocks, difficulties and failures. So, we decide to use high school completion rate and % of people who get Bachelor’s degree or......

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...Probability, Statistics, and Forecasting OPRE 433 Fall 2013 Regression Report Xie Gehui (gxx24@case.edu) Dec 2, 2013 I. Introduction The data set given contains more than one independent variable, so the target of our regression analysis is to build an appropriate multiple regression model. To realize this target, we have to build a multiple linear regression model to test the regression assumptions: model appropriateness, constant variance, independence, and normality. Certainly we need to modify the data set or the model itself to satisfy these assumptions, and at last get the model acceptable. In the original data set that we are going to deal with in this report, there are 20,640 observations of 8 explanatory variables labeled X1, X2, X3, X4, X5, X6, X7, X8 and 1 dependent variable labeled Y. All of the 9 variables are continuous. II. Method of analysis To check the model appropriateness assumption, we need to make sure the functional form is correct. The residual plot will show the pattern suggesting the form of an appropriate model. To check the validity of the constant variance assumption, we need to examine residual plots. A residual plot with a horizontal band appearance suggests that the spread of the error terms around 0 is not changing much as the horizontal plot value increases. Such a plot tells us that the constant variance assumption approximately holds. To check the independence assumption, we need to detect if any positive......

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...443e+02 35.259 < 2e-16 *** TV 1.130e+01 3.326e+00 3.396 0.000991 *** Radio 1.646e-01 2.462e+00 0.067 0.946826 Temp 1.891e+02 3.141e+01 6.019 3.12e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1833 on 97 degrees of freedom Multiple R-squared: 0.4571, Adjusted R-squared: 0.4403 F-statistic: 27.23 on 3 and 97 DF, p-value: 7.356e-13 a) Yes. Temp seems to have a significant impact on sales. By introducing the Temp variable, Radio’s level of significance drops outside of our accepted level. Tyler’s criticism seems to be justified. One would think that increased driving times would allow for greater penetration for Radio, but in the model it has no significance. | tv | Amount | 300 | Short | 11.422 | Overall(mf=3) | 34.27 | Profit | 10.28 | net | -289.72 | b) 5) Call: lm(formula = Sales ~ . - Week - week7 - week21 - week49, data = europet) Residuals: Min 1Q Median 3Q Max -2139.97 -681.28 -38.15 631.86 2121.55 Coefficients: Estimate Std. Error t value Pr(>|t|) ......

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...Acts 430 Regression Analysis In this project, we are required to forecast number of houses sold in the United States by creating a regression analysis using the SAS program. We initially find out the dependent variable which known as HSN1F. 30-yr conventional Mortgage rate, real import of good and money stock, these three different kinds of data we considered as independent variables, which can be seen as the factors will impact the market of house sold in USA. Intuitively, we thought 30-yr conventional mortgage rate is a significant factor that will influences our behavior in house sold market, which has a negative relation with number of house sold. When mortgage rate increases, which means people are paying relatively more to buy a house, which will leads to a decrease tendency in house sold market. By contrast, a lower interest rate would impulse the market. We believe that real import good and service is another factor that will causes up and down in house sold market. When a large amount of goods and services imported by a country, that means we give out a lot of money to other country. In other words, people have less money, the sales of houses decreased. Otherwise, less import of goods and services indicates an increase tendency in house sold market. We can see it also has a negative relationship with the number of house sold. Lastly, we have money stock as our third impact factor of house sold. We considered it has a positive relationship with the number of...

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...examining models? Variables change, this helps with estimating the values of functions for the different variable values. 2. Explain the purpose of simple linear regression and scatter diagrams. Please provide a simple linear regression model and define each variable used. A scattered diagram is a statistic tool that is used to show the relationship between two variables. The scattered diagram is a combination of simple linear regression line that is used to fit the model in between two variables. The line that is drawn in the scatter chart is a model that is formed from the simple linear regression the data provides. The line equation is as follows: y=mx+b. When the calculation is done from the line, the values for “m” and “b” (the slope and intercept) are calculated with the data that is used in the simple linear regression. An example of simple linear regression is as follows: car rental for 1 day is $100 M-Thur, weekend rates will vary depending on the demand of the rentals and the number of cars. The total cost for a car rental M-Wed = constant + variable portion = $300 + $25 (number of rentals on lot) Variables: The constant portion = $300 = total for car rental for 3 days The variable portion = $25 = direct cost of car rentals available Unknown variable = supply and demand 3. Describe multiple regression analysis and discuss potential uses for this model Multiple regressions are the extension of a simple linear regression. This regression is......

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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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...A) Estimated regression equation – First Order: y = β0 + β1x1 + β2x2 + ε Output of 1st Model | | | | | | | | | | | | | | Regression Statistics | | | | | | Multiple R | 0.763064634 | | | | | | R Square | 0.582267636 | SSR/SST | | ̂̂̂ | | | Adjusted R Square | 0.512645575 | | | | | | Standard Error | 547.737482 | | | | | | Observations | 15 | | | | | | | | | | | | | ANOVA | | | | | | | | df | SS | MS | F | Significance F | | Regression | 2 | 5018231.543 | 2509115.772 | 8.363263464 | 0.005313599 | | Residual | 12 | 3600196.19 | 300016.3492 | | | | Total | 14 | 8618427.733 | | | | | | | | | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Intercept | -20.35201243 | 652.7453202 | -0.031179101 | 0.975639286 | -1442.561891 | 1401.857866 | Age (x1) | 13.35044655 | 7.671676501 | 1.740225432 | 0.107375657 | -3.364700634 | 30.06559374 | Hours (x2) | 243.7144645 | 63.51173661 | 3.837313819 | 0.002363965 | 105.334278 | 382.0946511 | B) equation | ŷ= -20.3520124320994 + 13.3504465516772 x̂1 + 243.714464532425 x̂2 | C) Interpretation of β β̂1 = 13.35044655, If number of hours worked (x2) held fixed, we can estimate that every one-year increase in age (x1) the mean of annual earnings will increase by 13.35044655. β̂2 = 243.7144645, If age (X1) held fixed, we can estimate that every one hour (x2) of work increase, the mean of......

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...Using the simple regression model to explain the relationship between 3-Month T-bill rate and Dow Jones Index Index 1. Introduction………………………………………………3 2. Modeling the relationship between the 3-Month T-bill rates and Dow Jones Index (First Model)……………………3 3. Hypothesis and Testing…………………………………...4 4. Empirical Analysis………………………………………...5 5. Further Comparison………………………………………5 6. Conclusion…………………………………………………7 7. Appendix……………………………………………………8 8. Reference…………………………………………………..10 1. Introduction The 3-month T-bill rates and Dow Jones index are really close to the whole economic environment; the 3-month T-Bill rates are the preeminent default-risk-free rates in the US money market that is often used by researchers to proxy the risk-free asset whose existence is assumed by much conventional finance theory. Given their importance and visibility, it is not surprising that these interest rates has been studied extensively in economic and finance. Dow Jones Index, undoubtedly, is one of the most important economic indicators of the global financial market, This paper investigates the relationship between these two important economic data. In order to cover the business circle, the data which I choose is from 2001/01/01-2010/12/31, including the subprime lending crisis period. I use SAS and excel to get the information which indicates the relationship between these two representing data. 2. Modeling the relationship between the 3-Month......

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...Regression Paper Team RES/342 Research and Evaluation Teacher Date The Hypothesis Team C’s hypothesis is that the more years of education one receives the more a person can potentially earn in salary. The team will use the process of linear regression analysis to explain how the information is used and conduct a five-step test to see if the hypothesis proves true or false. Linear Regression Analysis Team C’s purpose of this research paper is to use a linear regression analysis test to determine if a significant linear relationship exists between an independent variable which is X, level or years of education, and a dependent variable Y, salaries earned or potentially earned. “It is used to determine the extent to which there is a linear relationship between a dependent variable and one or more independent variables,” (Statistically Significant Consulting, 2010, para. 1). Learning Team C will use the salary and education levels from the Wages and Wage Earners Data Set collected through access to the e-source link of University of Phoenix. For this test the dependent variable, Y, will represent the salary of the 100 participants and the independent variable, X, will represent the education of the 100 participants. How the Information is used This information will be used in a linear regression test to see if there is enough evidence to reject the null hypothesis that a higher education does not......

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