Statistical Techniques In Business And Economics Chapter 5 Answers
Ray Kowalewski
This textbook provides future data analysts with the tools, methods, and skills needed to answer data-focused, real life questions, to choose and apply appropriate methods to answer those questions, and to visualize and interpret results to support better decisions in business, economics, and public policy. Data wrangling and exploration, regression analysis, prediction with machine learning, and causal analysis are comprehensively covered, as well as when, why, and how the methods work, and how they relate to each other.
As the most effective way to communicate data analysis, running case studies play a central role in this textbook. Each case starts with an industry relevant question and answers it by using real-world data and applying the tools and methods covered in the textbook. Learning is then consolidated by over 360 practice questions and 120 data exercises. Extensive online resources, including raw and cleaned data and codes for all analysis in Stata, R, and Python are available on this site.
Data analysis is a process. It starts with formulating a question and collecting appropriate data, or assessing whether the available data can help answer the question. Then comes cleaning and organizing the data, tedious but essential tasks that affect the results of the analysis as much as any other step in the process. Exploratory data analysis gives context to the eventual results and helps deciding the details of the analytical method to be applied. The main analysis consists of choosing and implementing the method to answer the question, with potential robustness checks. Along the way, correct interpretation and effective presentation of the results are crucial. Carefully crafted data visualization help summarize our findings and convey key messages. The final task is to answer the original question, with potential qualifications and directions for future inquiries.
Our textbook equips future data analysts with the most important tools, methods and skills they need through the entire process of data analysis to answer data focused, real life questions. We cover all the fundamental methods that help along the process of data analysis. The textbook is divided into four parts covering data wrangling and exploration, regression analysis, prediction with machine learning, and causal analysis. We explain when, why, and how the various methods work, and how they are related to each other. MORE on content
A cornerstone of this textbook are 47 case studies spreading over one-third of our material. This reflects our view that working through case studies is the best way to learn data analysis. Each of our case studies starts with a relevant question and answers it in the end, using real life data and applying the tools and methods covered in the particular chapter. MORE on case studies
We share all raw and cleaned data we use in the case studies. We also share the codes that clean the data and produce all results, tables, and graphs in Stata, R, and Python so students can tinker with our code and compare the solutions in the different software. MORE on data and code
This textbook was written to be a complete course in data analysis. This textbook could be useful for university students in graduate programs as core text in applied statistics and econometrics, quantitative methods, or data analysis. It may also complement online courses that teach specific methods to give more context and explanation. Undergraduate courses can also make use of this textbook, even though the workload on students exceeds the typical undergraduate workload. Finally, the textbook can serve as a handbook for practitioners to guide them through all steps of real-life data analysis. MORE on why use this book?
Gbor Bks is an Assistant Professor at the Department of Economics and Business of the Central European University and director of the MS in Business Analytics program. He is a senior fellow at KRTK and a research affiliate at the Center for Economic Policy Research (CEPR). He published in top economics journals on multinational firm activities and productivity, business clusters, and innovation spillovers. He managed international data collection projects on firm performance and supply chains. He has done both policy advising (the European Commission, ECB) as well as private sector consultancy (in finance, business intelligence and real estate). He has taught graduate-level data analysis and economic geography courses since 2012. Personal website
Textbook for graduate students discusses the most important tools, methods, and skills necessary for carrying out a data analysis project, presenting case studies from around the world linking business or policy questions to decisions in data selection and the application of methods. Covers data collection and quality, exploratory data analysis and visualization generalizing from data, and hypothesis testing. Provides an overview of regression analysis, including probability models and time series regressions. Explores predictive analytics, cross-validation, tree-based machine learning methods, classification, and forecasting from time series data. Focuses on causal analysis, the potential outcomes framework and causal maps, difference-in-differences analysis, various panel data methods, and the event study approach.
Regression analysis, like most multivariate statistics, allows you to infer that there is a relationship between two or more variables. These relationships are seldom exact because there is variation caused by many variables, not just the variables being studied.
If you say that students who study more make better grades, you are really hypothesizing that there is a positive relationship between one variable, studying, and another variable, grades. You could then complete your inference and test your hypothesis by gathering a sample of (amount studied, grades) data from some students and use regression to see if the relationship in the sample is strong enough to safely infer that there is a relationship in the population. Notice that even if students who study more make better grades, the relationship in the population would not be perfect; the same amount of studying will not result in the same grades for every student (or for one student every time). Some students are taking harder courses, like chemistry or statistics; some are smarter; some study effectively; and some get lucky and find that the professor has asked them exactly what they understood best. For each level of amount studied, there will be a distribution of grades. If there is a relationship between studying and grades, the location of that distribution of grades will change in an orderly manner as you move from lower to higher levels of studying.
α and β are parameters, remaining constant as x and y change. α is the intercept and β is the slope. If the values of α and β are known, you can find the y that goes with any x by putting the x into the equation and solving. There can be functions where one variable depends on the values values of two or more other variables where x1 and x2 together determine the value of y. There can also be non-linear functions, where the value of the dependent variable (y in all of the examples we have used so far) depends on the values of one or more other variables, but the values of the other variables are squared, or taken to some other power or root or multiplied together, before the value of the dependent variable is determined. Regression allows you to estimate directly the parameters in linear functions only, though there are tricks that allow many non-linear functional forms to be estimated indirectly. Regression also allows you to test to see if there is a functional relationship between the variables, by testing the hypothesis that each of the slopes has a value of zero.
In most cases, even if the whole population had been gathered, the regression line would not go through every point. Most of the phenomena that business researchers deal with are not perfectly deterministic, so no function will perfectly predict or explain every observation.
Imagine that you wanted to study the estimated price for a one-bedroom apartment in Nelson, BC. You decide to estimate the price as a function of its location in relation to downtown. If you collected 12 sample pairs, you would find different apartments located within the same distance from downtown. In other words, you might draw a distribution of prices for apartments located at the same distance from downtown or away from downtown. When you use regression to estimate the parameters of price = f(distance), you are estimating the parameters of the line that connects the mean price at each location. Because the best that can be expected is to predict the mean price for a certain location, researchers often write their regression models with an extra term, the error term, which notes that many of the members of the population of (location, price of apartment) pairs will not have exactly the predicted price because many of the points do not lie directly on the regression line. The error term is usually denoted as ε, or epsilon, and you often see regression equations written:
In estimating the unknown parameters of the population for the regression line, we need to apply a method by which the vertical distances between the yet-to-be estimated regression line and the observed values in our sample are minimized. This minimized distance is called sample error, though it is more commonly referred to as residual and denoted by e. In more mathematical form, the difference between the y and its predicted value is the residual in each pair of observations for x and y. Obviously, some of these residuals will be positive (above the estimated line) and others will be negative (below the line). If we add all these residuals over the sample size and raise them to the power 2 in order to prevent the chance those positive and negative signs are cancelling each other out, we can write the following criterion for our minimization problem:
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