Analysis of a Larger Problem

In introducing multiple regression analysis, we used the Butler Trucking example extensively. The small size of this problem was an advantage in exploring introductory concepts but would make it difficult to illustrate some of the variable selection issues involved in model building. To provide an illustration of the variable selection procedures discussed in the

Variable Selection Procedures

In this section we discuss four variable selection procedures: stepwise regression, for­ward selection, backward elimination, and best-subsets regression. Given a data set with several possible independent variables, we can use these procedures to identify which in­dependent variables provide the best model. The first three procedures are iterative; at each step of the procedure a

Multiple Regression Approach to Experimental Design

In Section 15.7 we discussed the use of dummy variables in multiple regression analysis. In this section we show how the use of dummy variables in a multiple regression equation can provide another approach to solving experimental design problems. We will demonstrate the multiple regression approach to experimental design by applying it to the

Autocorrelation and the Durbin-Watson Test

Often, the data used for regression studies in business and economics are collected over time. It is not uncommon for the value of y at time t, denoted by y, to be related to the value of y at previous time periods. In such cases, we say autocorrelation (also called serial correlation) is present

Time Series Patterns

A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time. The measurements may be taken every hour, day, week, month, or year, or at any other regular interval.[1] The pattern of the data is an important factor in understanding how the

Forecast Accuracy with Time Series Analysis

In this section we begin by developing forecasts for the gasoline time series shown in Table 17.1 using the simplest of all the forecasting methods: an approach that uses the most recent week’s sales volume as the forecast for the next week. For instance, the dis­tributor sold 17 thousand gallons of gasoline in week

Moving Averages and Exponential Smoothing in Time Series Analysis

In this section, we discuss three forecasting methods that are appropriate for a time series with a horizontal pattern: moving averages, weighted moving averages, and exponential smoothing. These methods also adapt well to changes in the level of a horizontal pattern such as we saw with the extended gasoline sales time series (Table 17.2

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Trend Projection with Time Series Analysis

We present two forecasting methods in this section that are appropriate for time series exhibiting a trend pattern. First, we show how simple linear regression can be used to forecast a time series with a linear trend. Next we show how the curve-fitting capability of regression analysis can also be used to forecast time

Seasonality and Trend in Time Series Analysis

In this section we show how to develop forecasts for a time series that has a seasonal pattern. To the extent that seasonality exists, we need to incorporate it into our forecasting models to ensure accurate forecasts. We begin by considering a seasonal time series with no trend and then discuss how to model

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Time Series Decomposition

In this section we turn our attention to what is called time series decomposition. Time series decomposition can be used to separate or decompose a time series into seasonal, trend, and irregular components. While this method can be used for forecasting, its primary applicability is to get a better understanding of the time series.

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Sign Test

The sign test is a versatile nonparametric method for hypothesis testing that uses the binomial distribution with p = .50 as the sampling distribution. It does not require an assumption about the distribution of the population. In this section we present two applications of the sign test: one involving a hypothesis test about a

Wilcoxon Signed-Rank

In Chapter 10, we introduced a matched-sample experimental design where each of n experimental units provided a pair of observations, one from population 1 and one from population 2. The parametric test for this experiment requires quantitative data and the assumption that the differences between the paired observations are normally distributed. The t distribution

Mann-Whitney-Wilcoxon

In Chapter 10, we introduced a procedure for conducting a hypothesis test about the difference between the means of two populations using two independent samples, one from population 1 and one from population 2. This parametric test required quantitative data and the assumption that both populations had a normal distribution. In the case where

Kruskal-Wallis Test

In this section we extend the nonparametric procedures to hypothesis tests involving three or more populations. We considered a parametric test for this situation in Chapter 13 when we used quantitative data and assumed that the populations had nor­mal distributions with the same standard deviations. Based on an independent random sample from each population,

Rank Correlation

The Pearson product moment correlation coefficient introduced in Chapter 3 is a measure of the linear association between two variables using quantitative data. In this section, we provide a correlation measure of association between two variables when ordinal or rank-ordered data are available. The Spearman rank-correlation coefficient has been developed for this purpose. Let

Problem Formulation

The first step in the decision analysis process is problem formulation. We begin with a verbal statement of the problem. We then identify the decision alternatives, the uncertain future events, referred to as chance events, and the consequences associated with each decision alternative and each chance event outcome. Let us begin by considering a

Decision Making with Probabilities

Once we define the decision alternatives and the states of nature for the chance events, we can focus on determining probabilities for the states of nature. The classical method, the relative frequency method, or the subjective method of assigning probabilities may be used to identify these probabilities. After determining the appropriate probabilities, we show

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Decision Analysis with Sample Information

In applying the expected value approach, we showed how probability information about the states of nature affects the expected value calculations and thus the decision recommenda­tion. Frequently, decision makers have preliminary or prior probability assessments for the states of nature that are the best probability values available at that time. However, to make the

Computing Branch Probabilities Using Bayes’ Theorem

In Section 19.3 the branch probabilities for the PDC decision tree chance nodes were specified in the problem description. No computations were required to determine these probabilities. In this section we show how Bayes’ theorem can be used to compute branch probabilities for decision trees. The PDC decision tree is shown again in Figure

Price Relatives

The simplest form of a price index shows how the current price per unit for a given item compares to a base period price per unit for the same item. For example, Table 20.1 reports the cost of one gallon of gasoline for the years 2000 through 2017. To facilitate comparisons with other years,