Factors affecting online sales

Size: px
Start display at page:

Download "Factors affecting online sales"

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 front-end 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? 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 part-time 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 front-end 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 two-sample t-test for testing the null hypothesis stated above gives p-value < 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 p-value 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 front-end 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 Non-electrical Electrical Total No Yes Total Uses contractor Non-electrical 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 non-electrical 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 Non-electrical = π Electrical against H 1 : π Non-electrical π Electrical where π denotes the true proportion of firms who employ a contractor. A chi-squared test for testing the null hypothesis stated above gives p-value = 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 non-electrical 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 p-value 95% CI Intercept < Specialised staff < The p-value 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 p-value 95% CI Intercept < Specialised staff Specialised staff sq Page Epigeum Ltd, 2014

8 The p-value 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. part-time 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 p-value of <0.001 from a two-sample t-test 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 p-value 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 non-electrical (DIY/hardware and fashion) firms and electrical firms. A p-value of from a chi-squared test suggested that the true proportion is different for each sector. The percentage of non-electrical 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 p-value 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 (p-value 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 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 information

Regression Analysis: A Complete Example

Regression 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 information

CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression

CHAPTER 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 information

Multiple Linear Regression

Multiple 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 information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. 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 1-propZint 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 information

Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010

Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different

More information

Simple Linear Regression Inference

Simple 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 information

Module 5: Statistical Analysis

Module 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 information

Unit 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 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 information

Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics

Institute 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 information

2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or

2. 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 information

Chapter 7: Simple linear regression Learning Objectives

Chapter 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 information

Correlation and Simple Linear Regression

Correlation 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 information

Introduction to Regression and Data Analysis

Introduction 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 information

11. Analysis of Case-control Studies Logistic Regression

11. Analysis of Case-control Studies Logistic Regression Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

More information

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business 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, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

More information

MTH 140 Statistics Videos

MTH 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 information

Elements of statistics (MATH0487-1)

Elements of statistics (MATH0487-1) Elements of statistics (MATH0487-1) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis -

More information

Univariate Regression

Univariate 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 information

Bill 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 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 information

Simple linear regression

Simple 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 information

T 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 information

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics

Course 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, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

More information

DEPARTMENT 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 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 information

Part 2: Analysis of Relationship Between Two Variables

Part 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 information

2013 MBA Jump Start Program. Statistics Module Part 3

2013 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 information

Final Exam Practice Problem Answers

Final 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 information

Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Good 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 information

General Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n 1, n 2 ) 1.

General Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite 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 Welch-Satterthwaite formula or simpler df = min(n

More information

1) 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 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 information

Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 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 information

17. SIMPLE LINEAR REGRESSION II

17. 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 information

We extended the additive model in two variables to the interaction model by adding a third term to the equation.

We 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 information

1. 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

1. 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 information

August 2012 EXAMINATIONS Solution Part I

August 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 information

Data 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 Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................

More information

POLYNOMIAL AND MULTIPLE REGRESSION. Polynomial regression used to fit nonlinear (e.g. curvilinear) data into a least squares linear regression model.

POLYNOMIAL 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 information

The correlation coefficient

The 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 information

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate

More information

X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)

X 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 information

2. Simple Linear Regression

2. 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 information

Example: Boats and Manatees

Example: Boats and Manatees Figure 9-6 Example: Boats and Manatees Slide 1 Given the sample data in Table 9-1, find the value of the linear correlation coefficient r, then refer to Table A-6 to determine whether there is a significant

More information

Premaster Statistics Tutorial 4 Full solutions

Premaster 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 information

430 Statistics and Financial Mathematics for Business

430 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 information

Copyright 2010-2011 PEOPLECERT Int. Ltd and IASSC

Copyright 2010-2011 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, e-mail: info@peoplecert.org, www.peoplecert.org Copyright 2010-2011 PEOPLECERT

More information

Linear Models in STATA and ANOVA

Linear Models in STATA and ANOVA Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 4-2 A Note on Non-Linear Relationships 4-4 Multiple Linear Regression 4-5 Removal of Variables 4-8 Independent Samples

More information

Simple Linear Regression

Simple 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 information

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

NCSS 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 information

Elementary Statistics Sample Exam #3

Elementary 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 information

Predictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 R-Sq = 0.0% R-Sq(adj) = 0.

Predictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 R-Sq = 0.0% R-Sq(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 information

Estimation of σ 2, the variance of ɛ

Estimation 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 information

Unit 26: Small Sample Inference for One Mean

Unit 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 information

Lets suppose we rolled a six-sided die 150 times and recorded the number of times each outcome (1-6) occured. The data is

Lets suppose we rolled a six-sided die 150 times and recorded the number of times each outcome (1-6) occured. The data is In this lab we will look at how R can eliminate most of the annoying calculations involved in (a) using Chi-Squared tests to check for homogeneity in two-way tables of catagorical data and (b) computing

More information

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition

Bowerman, 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 Step-by-Step - Excel Microsoft Excel is a spreadsheet software application

More information

Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480

Week 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 information

A Primer on Forecasting Business Performance

A 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 information

Course Objective This course is designed to give you a basic understanding of how to run regressions in SPSS.

Course 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 information

business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar

business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel

More information

How Does My TI-84 Do That

How Does My TI-84 Do That How Does My TI-84 Do That A guide to using the TI-84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI-84 Do That A guide to using the TI-84 for statistics Table of Contents

More information

SPSS Tests for Versions 9 to 13

SPSS 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

Analysing 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 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 information

Session 9 Case 3: Utilizing Available Software Statistical Analysis

Session 9 Case 3: Utilizing Available Software Statistical Analysis Session 9 Case 3: Utilizing Available Software Statistical Analysis Michelle Phillips Economist, PURC michelle.phillips@warrington.ufl.edu With material from Ted Kury Session Overview With Data from Cases

More information

Fairfield Public Schools

Fairfield 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 information

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 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 information

STATISTICAL ANALYSIS WITH EXCEL COURSE OUTLINE

STATISTICAL 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 add-ins tools work on top of Excel, extending its power and abilities

More information

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

More information

Regression step-by-step using Microsoft Excel

Regression step-by-step using Microsoft Excel Step 1: Regression step-by-step 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 information

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall

More information

Statistical Models in R

Statistical Models in R Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova

More information

Statistical Models in R

Statistical Models in R Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Linear Models in R Regression Regression analysis is the appropriate

More information

Case Study in Data Analysis Does a drug prevent cardiomegaly in heart failure?

Case Study in Data Analysis Does a drug prevent cardiomegaly in heart failure? Case Study in Data Analysis Does a drug prevent cardiomegaly in heart failure? Harvey Motulsky hmotulsky@graphpad.com This is the first case in what I expect will be a series of case studies. While I mention

More information

Statistics courses often teach the two-sample t-test, linear regression, and analysis of variance

Statistics courses often teach the two-sample t-test, linear regression, and analysis of variance 2 Making Connections: The Two-Sample t-test, Regression, and ANOVA In theory, there s no difference between theory and practice. In practice, there is. Yogi Berra 1 Statistics courses often teach the two-sample

More information

Simple Linear Regression, Scatterplots, and Bivariate Correlation

Simple Linear Regression, Scatterplots, and Bivariate Correlation 1 Simple Linear Regression, Scatterplots, and Bivariate Correlation This section covers procedures for testing the association between two continuous variables using the SPSS Regression and Correlate analyses.

More information

Projects Involving Statistics (& SPSS)

Projects 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 information

An SPSS companion book. Basic Practice of Statistics

An 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 information

Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013

Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013 Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.1-1.6) Objectives

More information

Chapter 6: Multivariate Cointegration Analysis

Chapter 6: Multivariate Cointegration Analysis Chapter 6: Multivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie VI. Multivariate Cointegration

More information

A 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 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 information

Scatter Plots with Error Bars

Scatter Plots with Error Bars Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each

More information

SPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)

SPSS 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 information

SIMPLE LINEAR REGRESSION

SIMPLE LINEAR REGRESSION CHAPTER 2 SIMPLE LINEAR REGRESSION 2.1 I NTRO DU CTlO N We start with the simple case of studying the relationship between a response variable Y and a predictor variable XI. Since we have only one predictor

More information

Causal Forecasting Models

Causal Forecasting Models CTL.SC1x -Supply Chain & Logistics Fundamentals Causal Forecasting Models MIT Center for Transportation & Logistics Causal Models Used when demand is correlated with some known and measurable environmental

More information

Statistics in Retail Finance. Chapter 2: Statistical models of default

Statistics 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 information

Least Squares Estimation

Least Squares Estimation Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & David

More information

Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

More information

Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.

Below 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 information

Simple Predictive Analytics Curtis Seare

Simple 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 information

Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011

Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this

More information

Binary Diagnostic Tests Two Independent Samples

Binary 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 information

DATA INTERPRETATION AND STATISTICS

DATA INTERPRETATION AND STATISTICS PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE

More information

1-3 id id no. of respondents 101-300 4 respon 1 responsible for maintenance? 1 = no, 2 = yes, 9 = blank

1-3 id id no. of respondents 101-300 4 respon 1 responsible for maintenance? 1 = no, 2 = yes, 9 = blank Basic Data Analysis Graziadio School of Business and Management Data Preparation & Entry Editing: Inspection & Correction Field Edit: Immediate follow-up (complete? legible? comprehensible? consistent?

More information

STATISTICA Formula Guide: Logistic Regression. Table of Contents

STATISTICA Formula Guide: Logistic Regression. Table of Contents : Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary

More information

Independent t- Test (Comparing Two Means)

Independent t- Test (Comparing Two Means) Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent

More information

Introduction to Quantitative Methods

Introduction to Quantitative Methods Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................

More information

Module 5: Multiple Regression Analysis

Module 5: Multiple Regression Analysis Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

More information

Testing for Lack of Fit

Testing for Lack of Fit Chapter 6 Testing for Lack of Fit How can we tell if a model fits the data? If the model is correct then ˆσ 2 should be an unbiased estimate of σ 2. If we have a model which is not complex enough to fit

More information

STAT 350 Practice Final Exam Solution (Spring 2015)

STAT 350 Practice Final Exam Solution (Spring 2015) PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

More information

SUMAN DUVVURU STAT 567 PROJECT REPORT

SUMAN DUVVURU STAT 567 PROJECT REPORT SUMAN DUVVURU STAT 567 PROJECT REPORT SURVIVAL ANALYSIS OF HEROIN ADDICTS Background and introduction: Current illicit drug use among teens is continuing to increase in many countries around the world.

More information

An analysis appropriate for a quantitative outcome and a single quantitative explanatory. 9.1 The model behind linear regression

An analysis appropriate for a quantitative outcome and a single quantitative explanatory. 9.1 The model behind linear regression Chapter 9 Simple Linear Regression An analysis appropriate for a quantitative outcome and a single quantitative explanatory variable. 9.1 The model behind linear regression When we are examining the relationship

More information