Factors affecting online sales


 Wilfred Sharp
 2 years ago
 Views:
Transcription
1 Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4 Statistical modelling: Linear regression... 7 Conclusions... 8 Summary Recent anecdotal evidence suggests changes in sales patterns and in the level of investment in human resources dedicated to multichannel retailing 1. This study focuses on two aspects of multichannel retailing: level of online sales and level of investment. This research project aims to establish the levels of online sales achieved depending on retail sector and the number of specialised online marketing staff employed. Reasons behind the change in online sales levels between retail sectors and the drivers for this change are also an important part of the wider study, though this report only aims at establishing empirical associations between measured outcomes and their potential explanatory factors. Research questions 1. What levels of online sales are observed for each retail sector and how variable are they? 2. Is there a relationship between the use of frontend developer contractors and the retail sector? 3. To what extent does the number of specialised online marketing staff employed increase the levels of online sales? 1 1 Page Epigeum Ltd, 2014
2 The dataset The data consists of a sample of 36 firms from four locations across the United Kingdom. Information collected includes location of the firm, firm ID number, number of years in business, number of specialised staff currently employed (including parttime staff, hence not all figures are whole numbers), retail sector, proportion of sales generated online (as a percentage of total sales volume) and whether the firm uses external frontend developers (contractors) to supplement the number of internal programmers. The data has been stored in list format where each row contains data from an individual firm, and is ready for analysis. Figure 1 The dataset 2 Page Epigeum Ltd, 2014
3 Descriptive statistics: The exploratory stage The exploratory analysis checks that the data as computerised is of sufficient quality to be used for the analysis. There are a total of 36 firms, with a different number of firms from each retail sector. Table 1 shows summary statistics for the number of online sales and years in business. There are no missing values and no obvious errors such as negative sales figures or implausible numbers of years in business. There appear to be no oddities in the dataset and so we continue with the analysis. Table 1 Summary statistics for online sales and experience Measure Count Minimum Median Maximum Mean Standard deviation Online sales Years in business Figure 2 shows box plots of the online sales level for each retail sector. The fashion sector achieves the highest proportion of online sales, with a median of around 60%, which is about 15 percentage points higher than the DIY/hardware firms, and about 30 percentage points higher than the electrical firms. The lowest recorded online sales figure for the fashion sector was about 56%, which is higher than the highest recorded number of online sales for the electrical sector of about 43%. Figure 2 Box plots of online sales for each retail sector Figure 3 shows a scatter plot of online sales levels against the number of specialised staff employed, together with a straight line regression. It suggests that the number of online sales increases linearly with increasing numbers of specialised staff. The scatter plot also confirms that there are no obvious errors in the dataset. 3 Page Epigeum Ltd, 2014
4 Figure 3 Scatter plot of online sales against specialised staff Confidence intervals The sample mean percentage of online sales for DIY/hardware firms is 45.4% and a 95% confidence interval for their true mean percentage of online sales is (41.7%, 49.1%). The sample mean percentage of online sales for the electrical firms is 30% and a 95% confidence interval for their true mean percentage of online sales is (26.4%, 33.6%). The sample mean percentage of online sales for the fashion firms is 59.6% and a 95% confidence interval for their true mean percentage of online sales is (55.5%, 63.6%). Hypothesis tests Comparing means A table with summary statistics of the online sales variable is shown below for each retail sector: 4 Page Epigeum Ltd, 2014
5 Retail sector n Mean Standard deviation Minimum Median Maximum DIY/hardware Electrical Fashion We test the null hypothesis that the true mean percentage of online sales for DIY/hardware firms is the same as that for electrical firms, against the alternative hypothesis that the true mean percentage of online sales is different for the two retail sectors, i.e. we test: H 0 : μ DIY hardware μ Electrical = 0 against H 1 : μ DIY hardware μ Electrical 0 where µ denotes the true mean percentage of online sales for each retail sector respectively. A twosample ttest for testing the null hypothesis stated above gives pvalue < So we reject the null hypothesis in favour of the alternative. This suggests that the mean number of online sales is associated with these two retail sectors. The observed difference between the sample mean percentage of online sales by DIY/hardware firms and electrical firms is 15.44, with a standard error of the difference of A 95% confidence interval for the true difference between the two means is (10.48, 20.39). Note that the confidence interval for the true difference between means does not include zero, suggesting that the true mean percentage of online sales for DIY/hardware firms is higher than that for electrical firms. Analysis of variance Analysis of variance was used to compare all mean online sales percentages for all three retail sectors. The aim is to determine if there is any difference between the mean percentages of online sales for each role. So the null hypothesis is that there is no difference between the true mean percentage of online sales for the three retail sectors, and the alternative hypothesis is that at least two of the true means are different, i.e. we test: H 0 : μ DIY hardware = μ Electrical = μ Fashion against H 1 : At least two true mean online sales are not the same. The pvalue for testing the null hypothesis stated above is So we reject the null hypothesis in favour of the alternative and conclude that the mean percentage of sales generated online is related to retail sector. 5 Page Epigeum Ltd, 2014
6 Comparing proportions We investigate if the proportion of firms who use contractors differs between the electrical sector and nonelectrical sector. Tabulating the answer to the question Do you use external frontend developers to improve your online store's user interface? against type of sector, gives the following frequency table, also presented as percentages within each retail sector: Uses contractor Nonelectrical Electrical Total No Yes Total Uses contractor Nonelectrical Electrical Total No 42.9% 80.0% 58.3% Yes 57.1% 20.0% 41.7% Total 100.0% 100.0% 100.0% The observed proportion who use contractors for nonelectrical firms is 9/21 = 0.571, or 57.1%, while for electrical firms it is 3/15 = 0.2 or 20%. We assess if there is a statistical difference between the two retail sectors in the proportion of firms who use a contractor to improve their user interface. The null hypothesis we are testing is: H 0 : π Nonelectrical = π Electrical against H 1 : π Nonelectrical π Electrical where π denotes the true proportion of firms who employ a contractor. A chisquared test for testing the null hypothesis stated above gives pvalue = So we reject the null hypothesis in favour of the alternative, and conclude that the true proportions are different for the two retail sectors. This suggests that the proportion of firms who employ a contractor to improve their user interface is associated with their retail sector. The mean difference between the two proportions is = 0.371, with standard error of a difference of A 95% confidence interval for the true difference between the two proportions is (0.078, 0.664). 6 Page Epigeum Ltd, 2014
7 Note that the confidence interval for the true difference does not include zero, suggesting that the true proportion is higher for the nonelectrical firms than for the electrical firms. Statistical modelling: Linear regression We use linear regression to investigate the relationship between online sales (the response variable) and the number of specialised online marketing staff employed (the explanatory variable). Straight line regression model A straight line regression model was fitted to the data. The resulting table of regression coefficients is shown in Table 2. Table 2 Regression coefficients for a straight line regression model Parameter Estimate S.E. t pvalue 95% CI Intercept < Specialised staff < The pvalue for testing that the true value of the slope is zero is <0.001, so we reject the null hypothesis that the percentage of sales generated online is not related to the number of specialised staff employed. The two variables are statistically significantly related: as the number of specialised staff increases, so does the percentage of sales generated online. R 2 for the straight line regression model is This means that just over 60% of the total variability in online sales has been explained by the straight line regression model. Quadratic regression model A quadratic regression model was fitted to the data, giving a table of regression coefficients shown in Table 3. Table 3 Regression coefficients for a quadratic regression model Parameter Estimate S.E. t pvalue 95% CI Intercept < Specialised staff Specialised staff sq Page Epigeum Ltd, 2014
8 The pvalue testing the null hypothesis that a straight line model is adequate (true effect of number of specialised staff squared is zero) is 0.799, so we do not reject the null hypothesis. The addition of a quadratic term does not contribute statistically significantly to the regression model. Therefore, we adopt a straight line regression model as an adequate summary model of the observed relationship between online sales and number of specialised staff employed. The selected regression model Table 2 shows parameter estimates obtained from a straight line regression model, from which we can derive the straight line regression equation shown in Figure 3 as: Online sales = x Number of specialised staff Note that this equation is valid for a number of specialised staff employed between 0 and 3. Interpretation of parameter estimates Table 2 shows that the estimated increase in online sales for one more specialised staff member employed is 8.94 (percentage points). A 95% confidence interval for the true rate of change is (6.42, 11.47). Therefore, the estimated change in online sales for an additional half a member (i.e. parttime member) of specialised staff employed is 4.47 (percentage points) and a 95% confidence interval is (3.21, 5.73). The estimated intercept is 27.65: the predicted percentage of online sales for a firm with no specialised staff is 27.65%. As the observed range of specialised staff employed is 0 to 3, this prediction is meaningful. A 95% confidence interval for the true value of the intercept is (23.19, 32.11). So we are 95% confident that this interval contains the true percentage of online sales for firms that employ no specialised staff. Predictions Using the above equation, the predicted mean percentage of sales generated online by a firm with two members of specialised staff, is: x 2 = Conclusions There was evidence of an association between mean percentage of online sales and retail sector. First, a pvalue of <0.001 from a twosample ttest suggested that the true mean percentage of online sales is different between DIY/hardware firms and electrical firms. The mean percentage of online sales for DIY/hardware firms (45.4%) was higher by 15.4% than that for electrical firms (30%). The margin of error on this estimated difference is ±5%. 8 Page Epigeum Ltd, 2014
9 Further, a pvalue of from an analysis of variance suggested that the true mean percentage of online sales is significantly associated with all three retail sectors. There was evidence of an association between proportion of firms who employ a contractor to improve their user interface and retail sector when comparing nonelectrical (DIY/hardware and fashion) firms and electrical firms. A pvalue of from a chisquared test suggested that the true proportion is different for each sector. The percentage of nonelectrical firms who use a contractor (57.1%) was higher by 37.1% than that of electrical firms (20%). The margin of error on this estimated difference is 29.3%. There was evidence of an association between the number of specialised staff employed and online sales figures. A pvalue of <0.001 suggested that as the number of specialised staff increased, so did the online sales. The rate of increase in online sales was constant, i.e. followed a straight line. A straight line regression was found to be an adequate summary model, giving the following predictive equation: Online sales = x Number of specialised staff Each one more member of specialised staff results in an increase in online sales of 8.94%. The margin of error on this estimated increase is ±2.53%. This equation is valid for predictions of between 0 and 3 members of specialised staff. So the predicted percentage of online sales for firms with no specialised staff is 27.65%. A quadratic regression did not significantly improve the summary model (pvalue 0.799) over and above a straight line regression. 9 Page Epigeum Ltd, 2014
Analysis of categorical data: Course quiz instructions for SPSS
Analysis of categorical data: Course quiz instructions for SPSS The dataset Please download the Online sales dataset from the Download pod in the Course quiz resources screen. The filename is smr_bus_acd_clo_quiz_online_250.xls.
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationCHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression
Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationMultiple Linear Regression
Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is
More informationCurriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
More informationModule 5: Statistical Analysis
Module 5: Statistical Analysis To answer more complex questions using your data, or in statistical terms, to test your hypothesis, you need to use more advanced statistical tests. This module reviews the
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationSimple Linear Regression in SPSS STAT 314
Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,
More informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More information2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or
Simple and Multiple Regression Analysis Example: Explore the relationships among Month, Adv.$ and Sales $: 1. Prepare a scatter plot of these data. The scatter plots for Adv.$ versus Sales, and Month versus
More information11. Analysis of Casecontrol Studies Logistic Regression
Research methods II 113 11. Analysis of Casecontrol Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:
More informationChapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) 
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationBill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1
Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question
Stats: Test Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. ) Given H0: p 0% and Ha: p < 0%, determine
More informationAP Statistics 2002 Scoring Guidelines
AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression We are often interested in studying the relationship among variables to determine whether they are associated with one another. When we think that changes in a
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationIntroduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
More informationT O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGrawHill/Irwin, 2008, ISBN: 9780073319889. Required Computing
More informationStatistics 112 Regression Cheatsheet Section 1B  Ryan Rosario
Statistics 112 Regression Cheatsheet Section 1B  Ryan Rosario I have found that the best way to practice regression is by brute force That is, given nothing but a dataset and your mind, compute everything
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
More information93.4 Likelihood ratio test. NeymanPearson lemma
93.4 Likelihood ratio test NeymanPearson lemma 91 Hypothesis Testing 91.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental
More informationElements of statistics (MATH04871)
Elements of statistics (MATH04871) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis 
More information2013 MBA Jump Start Program. Statistics Module Part 3
2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More informationUnivariate Regression
Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is
More informationChapter 9. Section Correlation
Chapter 9 Section 9.1  Correlation Objectives: Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3 Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More informationIntroduction to Stata
Introduction to Stata September 23, 2014 Stata is one of a few statistical analysis programs that social scientists use. Stata is in the midrange of how easy it is to use. Other options include SPSS,
More informationWe extended the additive model in two variables to the interaction model by adding a third term to the equation.
Quadratic Models We extended the additive model in two variables to the interaction model by adding a third term to the equation. Similarly, we can extend the linear model in one variable to the quadratic
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationDEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9
DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,
More informationCourse Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGrawHill/Irwin, 2010, ISBN: 9780077384470 [This
More informationGood luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
More informationData Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools
Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................
More information1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ
STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material
More informationHYPOTHESIS TESTING: CONFIDENCE INTERVALS, TTESTS, ANOVAS, AND REGRESSION
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, TTESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate
More informationUsing Minitab for Regression Analysis: An extended example
Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to
More informationGeneral Method: Difference of Means. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n
More information17. SIMPLE LINEAR REGRESSION II
17. SIMPLE LINEAR REGRESSION II The Model In linear regression analysis, we assume that the relationship between X and Y is linear. This does not mean, however, that Y can be perfectly predicted from X.
More information2. Simple Linear Regression
Research methods  II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationttests and Ftests in regression
ttests and Ftests in regression Johan A. Elkink University College Dublin 5 April 2012 Johan A. Elkink (UCD) t and Ftests 5 April 2012 1 / 25 Outline 1 Simple linear regression Model Variance and R
More informationUCLA STAT 13 Statistical Methods  Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates
UCLA STAT 13 Statistical Methods  Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates 1. (a) (i) µ µ (ii) σ σ n is exactly Normally distributed. (c) (i) is approximately Normally
More informationPredictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 RSq = 0.0% RSq(adj) = 0.
Statistical analysis using Microsoft Excel Microsoft Excel spreadsheets have become somewhat of a standard for data storage, at least for smaller data sets. This, along with the program often being packaged
More informationPOLYNOMIAL AND MULTIPLE REGRESSION. Polynomial regression used to fit nonlinear (e.g. curvilinear) data into a least squares linear regression model.
Polynomial Regression POLYNOMIAL AND MULTIPLE REGRESSION Polynomial regression used to fit nonlinear (e.g. curvilinear) data into a least squares linear regression model. It is a form of linear regression
More informationThe correlation coefficient
The correlation coefficient Clinical Biostatistics The correlation coefficient Martin Bland Correlation coefficients are used to measure the of the relationship or association between two quantitative
More informationStatistical Models in R
Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 16233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova
More informationAugust 2012 EXAMINATIONS Solution Part I
August 01 EXAMINATIONS Solution Part I (1) In a random sample of 600 eligible voters, the probability that less than 38% will be in favour of this policy is closest to (B) () In a large random sample,
More informationElementary Statistics Sample Exam #3
Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to
More informationUnit 26: Small Sample Inference for One Mean
Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage
More informationEcon 371 Problem Set #3 Answer Sheet
Econ 371 Problem Set #3 Answer Sheet 4.3 In this question, you are told that a OLS regression analysis of average weekly earnings yields the following estimated model. AW E = 696.7 + 9.6 Age, R 2 = 0.023,
More informationX X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)
CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.
More informationBinary Diagnostic Tests Two Independent Samples
Chapter 537 Binary Diagnostic Tests Two Independent Samples Introduction An important task in diagnostic medicine is to measure the accuracy of two diagnostic tests. This can be done by comparing summary
More informationRegression, least squares
Regression, least squares Joe Felsenstein Department of Genome Sciences and Department of Biology Regression, least squares p.1/24 Fitting a straight line X Two distinct cases: The X values are chosen
More informationRegression. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between
More informationRegression stepbystep using Microsoft Excel
Step 1: Regression stepbystep using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression
More information430 Statistics and Financial Mathematics for Business
Prescription: 430 Statistics and Financial Mathematics for Business Elective prescription Level 4 Credit 20 Version 2 Aim Students will be able to summarise, analyse, interpret and present data, make predictions
More informationProjects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
More informationExample: Boats and Manatees
Figure 96 Example: Boats and Manatees Slide 1 Given the sample data in Table 91, find the value of the linear correlation coefficient r, then refer to Table A6 to determine whether there is a significant
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationAnalysing Questionnaires using Minitab (for SPSS queries contact ) Graham.Currell@uwe.ac.uk
Analysing Questionnaires using Minitab (for SPSS queries contact ) Graham.Currell@uwe.ac.uk Structure As a starting point it is useful to consider a basic questionnaire as containing three main sections:
More informationBowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology StepbyStep  Excel Microsoft Excel is a spreadsheet software application
More informationSimple Regression and Correlation
Simple Regression and Correlation Today, we are going to discuss a powerful statistical technique for examining whether or not two variables are related. Specifically, we are going to talk about the ideas
More informationSTATISTICAL ANALYSIS WITH EXCEL COURSE OUTLINE
STATISTICAL ANALYSIS WITH EXCEL COURSE OUTLINE Perhaps Microsoft has taken pains to hide some of the most powerful tools in Excel. These addins tools work on top of Excel, extending its power and abilities
More informationPremaster Statistics Tutorial 4 Full solutions
Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationCopyright 20102011 PEOPLECERT Int. Ltd and IASSC
PEOPLECERT  Personnel Certification Body 3 Korai st., 105 64 Athens, Greece, Tel.: +30 210 372 9100, Fax: +30 210 372 9101, email: info@peoplecert.org, www.peoplecert.org Copyright 20102011 PEOPLECERT
More informationSimple Predictive Analytics Curtis Seare
Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use
More informationA Primer on Forecasting Business Performance
A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.
More informatione = random error, assumed to be normally distributed with mean 0 and standard deviation σ
1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.
More informationLinear Models in STATA and ANOVA
Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 42 A Note on NonLinear Relationships 44 Multiple Linear Regression 45 Removal of Variables 48 Independent Samples
More informationStatistics  Written Examination MEC Students  BOVISA
Statistics  Written Examination MEC Students  BOVISA Prof.ssa A. Guglielmi 26.0.2 All rights reserved. Legal action will be taken against infringement. Reproduction is prohibited without prior consent.
More informationSimple Linear Regression
STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze
More informationLesson Lesson Outline Outline
Lesson 15 Linear Regression Lesson 15 Outline Review correlation analysis Dependent and Independent variables Least Squares Regression line Calculating l the slope Calculating the Intercept Residuals and
More informationSPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
More informationA Review of Cross Sectional Regression for Financial Data You should already know this material from previous study
A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study But I will offer a review, with a focus on issues which arise in finance 1 TYPES OF FINANCIAL
More informationLets suppose we rolled a sixsided die 150 times and recorded the number of times each outcome (16) occured. The data is
In this lab we will look at how R can eliminate most of the annoying calculations involved in (a) using ChiSquared tests to check for homogeneity in twoway tables of catagorical data and (b) computing
More informationStatistical Testing of Randomness Masaryk University in Brno Faculty of Informatics
Statistical Testing of Randomness Masaryk University in Brno Faculty of Informatics Jan Krhovják Basic Idea Behind the Statistical Tests Generated random sequences properties as sample drawn from uniform/rectangular
More informationStatistics in Retail Finance. Chapter 2: Statistical models of default
Statistics in Retail Finance 1 Overview > We consider how to build statistical models of default, or delinquency, and how such models are traditionally used for credit application scoring and decision
More informationAP Statistics 2001 Solutions and Scoring Guidelines
AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use
More informationEstimation of σ 2, the variance of ɛ
Estimation of σ 2, the variance of ɛ The variance of the errors σ 2 indicates how much observations deviate from the fitted surface. If σ 2 is small, parameters β 0, β 1,..., β k will be reliably estimated
More informationBelow is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.
Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data
More informationAn SPSS companion book. Basic Practice of Statistics
An SPSS companion book to Basic Practice of Statistics SPSS is owned by IBM. 6 th Edition. Basic Practice of Statistics 6 th Edition by David S. Moore, William I. Notz, Michael A. Flinger. Published by
More informationSydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.
Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under
More informationOutline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics
Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public
More informationCourse Objective This course is designed to give you a basic understanding of how to run regressions in SPSS.
SPSS Regressions Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course is designed
More informationHow Does My TI84 Do That
How Does My TI84 Do That A guide to using the TI84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI84 Do That A guide to using the TI84 for statistics Table of Contents
More informationHow to Conduct a Hypothesis Test
How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some
More informationSPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS)
SPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One
More informationWeek TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480
1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500
More informationExercise 1.12 (Pg. 2223)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More information, has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results.
BA 275 Review Problems  Week 9 (11/20/0611/24/06) CD Lessons: 69, 70, 1620 Textbook: pp. 520528, 111124, 133141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An
More informationSPSS Tests for Versions 9 to 13
SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list
More information