Regression Analysis and a Data Analysis Overview
Regression Analysis and a Data Analysis Overview
In data analysis there is often one or a small number of key variables that become the focus of the study. When a new product or concept is being explored, for example, one of the key variables is usually the respondent's attitude or intentions toward it. Is it something that the respondent would consider buying and/or using? The goal may be to predict the ultimate usage of the product or concept under a variety of conditions. Another goal might be to understand what causes high intentions so that when the product does emerge the marketing program can be adjusted to improve the success probability.
Consider the HMO study. In this study, the intention to enroll was one of the variables of interest. One motivation was prediction: to predict the enrollment if the plan were implemented. Thus, the intention question was analyzed to help predict the acceptance of the concept among the sample of respondents.
However, it would be desirable to determine how the intentions to enroll were related to distance to the HMO. If such a relationship were known it might be possible to predict intentions for neighborhood areas just by knowing the distance to the HMO. Similarly, if the relationship
between enrollment intentions and the health plan now used were known, then some knowledge would be available about the possible intentions of others just by knowing their health plan. Furthermore, if the relationship between the coverage of the HMO (what services are included) and people's intentions were known, then the prediction could be adjusted depending upon the coverage actually used when the plan was implemented.
Regression analysis provides a tool that can quantify such relationships. Further, unlike cross-tabs and other association measures, which deal only with two variables, regression analysis can integrate the relationship of intentions with two, three, or more variables simultaneously. Thus, a regression analysis could generate a model that could address the following question: if there is a group of people who now live five miles from the proposed HMO and who now belong to Blue Cross, what enrollment intention level would this group have regarding the HMO plan if the coverage is comprehensive? Since nearly all management decisions depend on accurate predictions of key variables, regression analysis can be an extremely practical and powerful tool.
Prediction is not the only reason that a knowledge of the relationship between intentions and other variables is useful in the HMO study. Another motivation is to gain understanding of the relationship so that the marketing program can be adjusted. If the relationship between intentions and the distance to the HMO is known, then a decision as to where to focus the marketing program geographically can be made more intelligently. It would make little sense to expend marketing effort on groups with little potential. Further, the relationship of intentions to the health plan of participants might provide information as to what competitive health plans are most vulnerable and could help guide the development of the marketing program. The relationship between intentions and an HMO characteristic such as coverage could influence the exact type of plan introduced. A "product feature" such as coverage should be specified so that the costs of the feature can be balanced with its impact on enrollment.
Regression analysis not only quantifies individual relationships but it also provides statistical control. Thus, it can quantify the relationship between intentions and distance while statistically controlling for the health plan and coverage variables.
Regression analysis, like conjoint analysis, is an analysis of dependence technique, since it involves a dependent variable as the focus of the analysis. The dependent variable is predicted by or explained by the remaining ones, the independent variables. For example, in the HMO study the enrollment intentions would be the dependent variable. The distance to the HMO, the existing health plan, and the HMO planned coverage would be three independent variables. The independent variable sometimes is called the predictor variable because, when prediction is the goal, it helps to predict values of the dependent variable. It also sometimes is called the explanatory variable because it might explain variation in the dependent variable. The analysis of dependence is oriented toward either prediction or gaining understanding of the relationships between a set of independent variables and a dependent variable.
Regression analysis will be described in detail in this chapter. The chapter will also include a brief description of two regression analysis extensions, simultaneous equation regression analysis and unobservable variables in regression analysis, and two other analysis of dependence techniques, discriminant analysis, and AID. The chapter will conclude with an overview of data analysis. A variety of techniques have been covered in the data analysis chapters in Part III and Part IV. It will be useful to position these techniques within the toted data analysis process. In doing so, the steps of data analysis presented in Chapter 13 will be expanded and modified.
In describing regression analysis, special emphasis will be placed on identifying the inputs that are required, the outputs that are generated, and the important assumptions and limitations that are associated with it. The outputs are generally of two types: (1) a measure of how well prediction is accomplished and (2) the measurement of the relationship between the various explanatory variables and the dependent variables. The outputs often will have associated with them some statistical tests of significance.
In data analysis there is often one or a small number of key variables that become the focus of the study. When a new product or concept is being explored, for example, one of the key variables is usually the respondent's attitude or intentions toward it. Is it something that the respondent would consider buying and/or using? The goal may be to predict the ultimate usage of the product or concept under a variety of conditions. Another goal might be to understand what causes high intentions so that when the product does emerge the marketing program can be adjusted to improve the success probability.
Consider the HMO study. In this study, the intention to enroll was one of the variables of interest. One motivation was prediction: to predict the enrollment if the plan were implemented. Thus, the intention question was analyzed to help predict the acceptance of the concept among the sample of respondents.
However, it would be desirable to determine how the intentions to enroll were related to distance to the HMO. If such a relationship were known it might be possible to predict intentions for neighborhood areas just by knowing the distance to the HMO. Similarly, if the relationship
between enrollment intentions and the health plan now used were known, then some knowledge would be available about the possible intentions of others just by knowing their health plan. Furthermore, if the relationship between the coverage of the HMO (what services are included) and people's intentions were known, then the prediction could be adjusted depending upon the coverage actually used when the plan was implemented.
Regression analysis provides a tool that can quantify such relationships. Further, unlike cross-tabs and other association measures, which deal only with two variables, regression analysis can integrate the relationship of intentions with two, three, or more variables simultaneously. Thus, a regression analysis could generate a model that could address the following question: if there is a group of people who now live five miles from the proposed HMO and who now belong to Blue Cross, what enrollment intention level would this group have regarding the HMO plan if the coverage is comprehensive? Since nearly all management decisions depend on accurate predictions of key variables, regression analysis can be an extremely practical and powerful tool.
Prediction is not the only reason that a knowledge of the relationship between intentions and other variables is useful in the HMO study. Another motivation is to gain understanding of the relationship so that the marketing program can be adjusted. If the relationship between intentions and the distance to the HMO is known, then a decision as to where to focus the marketing program geographically can be made more intelligently. It would make little sense to expend marketing effort on groups with little potential. Further, the relationship of intentions to the health plan of participants might provide information as to what competitive health plans are most vulnerable and could help guide the development of the marketing program. The relationship between intentions and an HMO characteristic such as coverage could influence the exact type of plan introduced. A "product feature" such as coverage should be specified so that the costs of the feature can be balanced with its impact on enrollment.
Regression analysis not only quantifies individual relationships but it also provides statistical control. Thus, it can quantify the relationship between intentions and distance while statistically controlling for the health plan and coverage variables.
Regression analysis, like conjoint analysis, is an analysis of dependence technique, since it involves a dependent variable as the focus of the analysis. The dependent variable is predicted by or explained by the remaining ones, the independent variables. For example, in the HMO study the enrollment intentions would be the dependent variable. The distance to the HMO, the existing health plan, and the HMO planned coverage would be three independent variables. The independent variable sometimes is called the predictor variable because, when prediction is the goal, it helps to predict values of the dependent variable. It also sometimes is called the explanatory variable because it might explain variation in the dependent variable. The analysis of dependence is oriented toward either prediction or gaining understanding of the relationships between a set of independent variables and a dependent variable.
Regression analysis will be described in detail in this chapter. The chapter will also include a brief description of two regression analysis extensions, simultaneous equation regression analysis and unobservable variables in regression analysis, and two other analysis of dependence techniques, discriminant analysis, and AID. The chapter will conclude with an overview of data analysis. A variety of techniques have been covered in the data analysis chapters in Part III and Part IV. It will be useful to position these techniques within the toted data analysis process. In doing so, the steps of data analysis presented in Chapter 13 will be expanded and modified.
In describing regression analysis, special emphasis will be placed on identifying the inputs that are required, the outputs that are generated, and the important assumptions and limitations that are associated with it. The outputs are generally of two types: (1) a measure of how well prediction is accomplished and (2) the measurement of the relationship between the various explanatory variables and the dependent variables. The outputs often will have associated with them some statistical tests of significance.
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