INTRODUCTION

I.1 STATISTICS IN PRACTICE

Statistics is used in many fields of application since it provides an effective way to analyze quantitative information. Some examples include:

• A pharmaceutical company is developing a new drug for treating a particular disease more effectively. How might statistics help you decide whether the drug will be safe and effective if brought to market?

  Clinical trials involve large-scale statistical studies of people-usually both patients with the disease and healthy volunteers-who are assessed for their response to the drug. To determine that the drug is both safe and effective requires careful statistical analysis of the trial results, which can involve controlling for the personal characteristics of the people (e.g., age, gender, health history) and possible placebo effects, comparisons with alternative treatments, and so on.

• A manufacturing firm is not getting paid by its customers in a timely manner-this costs the firm money on lost interest. You've collected recent data for the customer accounts on amount owed, number of days since the customer was billed, and size of the customer (small, medium, large). How might statistics help you improve the on-time payment rate?

  You can use statistics to find out whether there is an association between the amount owed and the number of days and/or size. For example, there may be a positive association between amount owed and number of days for small and medium-sized customers but not for large-sized customers-thus it may be more profitable to focus collection efforts on small and medium-sized customers billed some time ago, rather than on large-sized customers or customers billed more recently.

• A firm makes scientific instruments and has been invited to make a sealed bid on a large government contract. You have cost estimates for preparing the bid and fulfilling the contract, as well as historical information on similar previous contracts on which the firm has bid (some successful, others not). How might statistics help you decide how to price the bid?

  You can use statistics to model the association between the success/failure of past bids and variables such as bid cost, contract cost, bid price, and so on. If your model proves useful for predicting bid success, you could use it to set a maximum price at which the bid is likely to be successful.

• As an auditor, you'd like to determine the number of price errors in all of a company's invoices-this will help you detect whether there might be systematic fraud at the company. It is too time-consuming and costly to examine all of the company's invoices, so how might statistics help you determine an upper bound for the proportion of invoices with errors?

  Statistics allows you to infer about a population from a relatively small random sample of that population. In this case, you could take a sample of 100 invoices, say, to find a proportion, p, such that you could be 95% confident that the population error rate is less than that quantity p.

• A firm manufactures automobile parts and the factory manager wants to get a better understanding of overhead costs. You believe two variables in particular might contribute to cost variation: machine hours used per month and separate production runs per month. How might statistics help you to quantify this information?

  You can use statistics to build a multiple linear regression model that estimates an equation relating the variables to one another. Among other things you can use the model to determine how much cost variation can be attributed to the two cost drivers, their individual effects on cost, and predicted costs for particular values of the cost drivers.

• You work for a computer chip manufacturing firm and are responsible for forecasting future sales. How might statistics be used to improve the accuracy of your forecasts?

  Statistics can be used to fit a number of different forecasting models to a time series of sales figures. Some models might just use past sales values and extrapolate into the future, while others might control for external variables such as economic indices. You can use statistics to assess the fit of the various models, and then use the best-fitting model, or perhaps an average of the few best-fitting models, to base your forecasts on.

• As a financial analyst, you review a variety of financial data, such as price/ earnings ratios and dividend yields, to guide investment recommendations. How might statistics be used to help you make buy, sell, or hold recommendations for individual stocks?

  By comparing statistical information for an individual stock with information about stock market sector averages, you can draw conclusions about whether the stock is overvalued or undervalued. Statistics is used for both "technical analysis" (which considers the trading patterns of stocks) and "quantitative analysis" (which studies economic or company-specific data that might be expected to affect the price or perceived value of a stock).

• You are a brand manager for a retailer and wish to gain a better understanding of the association between promotional activities and sales. How might statistics be used to help you obtain this information and use it to establish future marketing strategies for your brand?

  Electronic scanners at retail checkout counters and online retailer records can provide sales data and statistical summaries on promotional activities such as discount pricing and the use of in-store displays or e-commerce websites. Statistics can be used to model these data to discover which product features appeal to particular market segments and to predict market share for different marketing strategies.

• As a production manager for a manufacturer, you wish to improve the overall quality of your product by deciding when to make adjustments to the production process, for example, increasing or decreasing the speed of a machine. How might statistics be used to help you make those decisions?

  Statistical quality control charts can be used to monitor the output of the production process. Samples from previous runs can be used to determine when the process is "in control." Ongoing samples allow you to monitor when the process goes out of control, so that you can make the adjustments necessary to bring it back into control.

• As an economist, one of your responsibilities is providing forecasts about some aspect of the economy, for example, the inflation rate. How might statistics be used to estimate those forecasts optimally?

  Statistical information on various economic indicators can be entered into computerized forecasting models (also determined using statistical methods) to predict inflation rates. Examples of such indicators include the producer price index, the unemployment rate, and manufacturing capacity utilization.

• As general manager of a baseball team with limited financial resources, you'd like to obtain strong, yet undervalued players. How might statistics help you to do this?

  A wealth of statistical information on baseball player performance is available, and objective analysis of these data can reveal information on those players most likely to add value to the team (in terms of winning games) relative to a player's cost. This field of statistics even has its own name, sabermetrics.

I.2 Learning Statistics

• What is this book about?

  This book is about the application of statistical methods, primarily regression analysis and modeling, to enhance decision-making. Regression analysis is by far the most used statistical methodology in real-world applications. Furthermore, many other statistical techniques are variants or extensions of regression analysis, so once you have a firm foundation in this methodology, you can approach these other techniques without too much additional difficulty. In this book we show you how to apply and interpret regression models, rather than deriving results and formulas (there is no calculus in the book).

• Why are non-math major students required to study statistics?

  In many aspects of modern life, we have to make decisions based on incomplete information (e.g., health, climate, economics, business). This book will help you to understand, analyze, and interpret such data in order to make informed decisions in the face of uncertainty. Statistical theory allows a rigorous, quantifiable appraisal of this uncertainty.

• How is the book organized?

  Chapter 1 reviews the essential details of an introductory statistics course necessary for use in later chapters. Chapter 2 covers the simple linear regression model for analyzing the linear association between two variables (a "response" and a "predictor"). Chapter 3 extends the methods of Chapter 3 to multiple linear regression where there can be more than one predictor variable. Chapters 4 and 5 provide guidance on building regression models, including transforming variables, using interactions, incorporating qualitative information, and diagnosing problems. Chapter 6 (www.wiley.com/go/pardoe/AppliedRegressionModeling3e) contains three case studies that apply the linear regression modeling techniques considered in this book to examples on real estate prices, vehicle...