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This note, the first in a series on regression analysis, introduces the simple linear model (one X-variable), together with least squares, as a procedure for estimating the coefficients in the model. The standard error of estimate, adjusted R-square, and standard error of the coefficients are all introduced and explained. The presentation of formulas is kept to a minimum, and an illustrative example is used throughout the note. . This note, the first in a series on regression analysis, introduces the simple linear model (one X-variable), together with least squares, as a procedure for estimating the coefficients in the model. The standard error of estimate, adjusted R-square, and standard error of the coefficients are all introduced and explained. The presentation of formulas is kept to a minimum, and an illustrative example is used throughout the note.

Five carefully constructed problems illustrate the concepts of second-market discounting, price skimming, limit pricing, random discounting, premium pricing, and bundling.

This case concerns the promotional activities of Nashua Photo, the nation's largest mail-order photofinishing firm. Discount-price mailers (inserted in local newspapers, for example) were used to generate new customers, but also allowed existing customers to pay a lower price. Students must evaluate not only the results of last quarter's 125 separate promotions in light of this "leakage," but also the appropriateness of discount-price mailers within Nashua's marketing mix.

Crutchfield, a large U.S. mail-order firm specializing in consumer electronics and personal computers, must evaluate the results of a recent "prospecting" mailing to a rented list of names. A determination of the mailing requires the calculation of the lifetime value of the new customers acquired. Case data on repurchase probabilities (broken out by recency and frequency) support such a calculation. The case can also be used to introduce the RFM (recency, frequency, monetary value) framework for valuing customers.

The director of marketing and operations for a financial newsletter must deal with a host of issues that surround the practice of renting mailing lists and soliciting new subscribers by direct mail. The case can be used to introduce the concept and calculation of customer lifetime value.

The B case describes Frank Lockfeld building a spreadsheet model that captures the essence of the discussion in the A case. Since this is a difficult model to build, we recommend using the B case when teaching the Calambra Olive Oil sequence early in a module on Monte Carlo simulation. The model, which is also available electronically and should be distributed with the B case, is set up to evaluate scenarios and compare (in multiple columns) the affect of different order quantities for the specified scenario. To turn the model into a simulation model, all the students need do is replace the scenario drivers with probability distributions. Note: the C case may be used in place of--NOT IN ADDITION TO--the B case. Rather than evaluate different order quantities in columns, the C case uses data tables.

Spreadsheet Supplement for UV6185

Supplement for UV3331

The plant manager of the Edgcomb Metals facility at Troy, Virginia is confronted with complaints that the current driver wage system-a guaranteed eight-hour day with time and a half for overtime-rewards drivers who "take their time" on daily assigned delivery routes. To investigate these claims, the plant manager compiles data on total hours, number of miles, and number of stops for several delivery runs made by each of two drivers-one recognized as the best and most conscientious, and the other recognized as the slowest. A supplemental handout (OM-0576) contains the results of a regression analysis of the data to facilitate a comparison of the two drivers and to suggest a method for developing standard times. (The B case is OM-0562, and the C case is OM-0571.)

This case discusses the so-called sophomore jinx: professional athletes who perform superbly as rookies never seem to do as well in their second--sophomore--season. The case gives performance data for Rookie of the Year award winners in major-league baseball through 2003 (29 pitchers and 83 nonpitchers). Data cover both the first and second years. Students must decide for themselves, based on the data, whether the sophomore jinx is real or imagined.

The manager of the Revenue Enhancement Department of an airline has to decide the optimal number of seats to reserve for discount customers on a particular flight. Historical data are given, as well as probability distributions of demand for both full and discount fares, in order to help make the decision. (The B case is QA-0340.)

Amore must set the fill-target for its eight-ounce macaroni and cheese pie. Unless five sample pies taken every 20 minutes average more than eight ounces, the entire 20-minute batch must be rejected. The case provides enough information to make an economic decision on the fill target. The case may be used to introduce the distribution of a sample average.

Supplement for UV6120

The general manager of the Oakland A's professional baseball team must evaluate two salary-and-bonus plans proposed by the A's star pitcher (see UV3696). The plans call for the pitcher to receive a bonus if the next season's home attendance exceeds a specified amount. Historical data are provided on team performance (number of games won), attendance, and the general manager's preseason forecasted number of wins.

This case describes the situation faced by the general manager of the A's at the end of the 1980 baseball season. The A's star pitcher, in negotiating his contract, claims that attendance was noticeably higher at games in which he was the starting pitcher. Game-by-game data for the 1980 season on home attendance and ten variables affecting attendance are given. The case is suited for use near the end of a module on regression. It can be used to (1) review the t-test for a difference in means and relate the difference to regression with a dummy variable, (2) illustrate the importance of a model-building framework, even if used to evaluate someone else's models, (3) illustrate the use of dummy variables, and (4) point out the difference between conditional and marginal inference. The supplement, QA-0313, contains the results of several regression analyses of the A's 1980 home-attendance data and may be used with the A case to facilitate analysis of the situation. (The B case is UV3698.)

George Lasiter sells special-events T-shirts, and must decide how many to order for an upcoming concert. He has high, medium, and low estimates of both concert attendance and the percentage of attendees who will want a shirt. In addition, he has assessed the relative likelihoods of each estimate. The case can be used to introduce or reinforce the fundamental issues surrounding decision-making under uncertainty.

Thomas Stearns must decide whether to continue with planned software development and risk missing the completion deadline on a $20 million project or bite the bullet and make some costly hardware changes that will virtually eliminate the risk of missing the deadline. This introductory decision analysis case: (1) contains a compound (square-circle-square) decision, (2) encourages a discussion of the meaning of probability, and (3) requires the use of sensitivity analysis to handle the unspecified costs of missing the deadline.

In this case, the managers of quality assurance must specify a fill-target for individual bottles of a new blood-pressure medicine. Higher targets lead to higher material costs but fewer seconds.

This case describes two shipping firms in the midst of a price war over the market for containerized shipping to and from a small Caribbean island. The situation is a classic duopoly. The case presents a table of contributions to both firms as a function of their prices. This table serves as a basis by which the class can explore the concepts of Nash equilibrium, price leadership, and prisoners' dilemma. See also ''Lesser Antilles Lines (B)'' and ''Lesser Antilles Lines (C).''

This note illustrates several data-analysis techniques that can be used to compare two groups of interval data.