Regression Analysis and a Data Analysis Overview - Summary
Regression Analysis and a Data Analysis Overview - Summary
Applications
Regression analysis is used (1) to predict the dependent variable, given knowledge of independent variable values, and (2) to gain an understanding of the relationship between trie dependent variable and independent variables.
Inputs
The model inputs required are the variable values for the dependent variable and the independent variables (although actually only the intervariable correlations are enough).
Outputs
The regression model will output regression coefficients—and their associated beta coefficient and r-values—that can be used to evaluate the strength of the relationship between the respective independent variable and the dependent variable. The model automatically controls statistically for the other independent variables. Thus, a regression coefficient represents the effect of one independent variable with the other independent variables held constant. Another output is the r2 value, which provides a measure of the predictive ability of the model.
Statistical Tests
The hypothesis that the regression parameter is zero and the parameter estimate is nonzero only because of sampling is based on the t-value.
Assumptions
The most important assumption is that the selected independent variables do, in fact, explain or predict the dependent variable, that there are no important variables omitted. In creating and evaluating regression models the following questions are appropriate: "Do these independent variables influence the dependent variable? Do any lack any logical justification for being in the model? Are any variables omitted that logically should be in the model?" A second assumption is that the relationship between the independent variables and the dependent variable is linear and additive. A third assumption is that there is a "random" error term that absorbs the effects of measurement error and the influences of variables not included in the regression equation.
Limitations
First, a knowledge of a regression coefficient and its t-value can suggest the extent of association or influence that an independent variable has on the dependent variable. However, if an omitted variable is correlated with the independent variable, the regression coefficient will reflect the impact of the omitted variables on the dependent variables. A second limitation is that the model is based on collected data that represent certain environmental conditions. If those conditions change, the model may no longer reflect the current situations and can lead to erroneous judgments. Third, the ability of the model to predict, as reflected by r2, can become significantly reduced if the prediction is based on values of the independent variables that are extreme in comparison to the independent variable values used tc estimate the model parameters. Fourth, the model is limited by the methodology associated with the data collection, including the sample size and measures used.
Applications
Regression analysis is used (1) to predict the dependent variable, given knowledge of independent variable values, and (2) to gain an understanding of the relationship between trie dependent variable and independent variables.
Inputs
The model inputs required are the variable values for the dependent variable and the independent variables (although actually only the intervariable correlations are enough).
Outputs
The regression model will output regression coefficients—and their associated beta coefficient and r-values—that can be used to evaluate the strength of the relationship between the respective independent variable and the dependent variable. The model automatically controls statistically for the other independent variables. Thus, a regression coefficient represents the effect of one independent variable with the other independent variables held constant. Another output is the r2 value, which provides a measure of the predictive ability of the model.
Statistical Tests
The hypothesis that the regression parameter is zero and the parameter estimate is nonzero only because of sampling is based on the t-value.
Assumptions
The most important assumption is that the selected independent variables do, in fact, explain or predict the dependent variable, that there are no important variables omitted. In creating and evaluating regression models the following questions are appropriate: "Do these independent variables influence the dependent variable? Do any lack any logical justification for being in the model? Are any variables omitted that logically should be in the model?" A second assumption is that the relationship between the independent variables and the dependent variable is linear and additive. A third assumption is that there is a "random" error term that absorbs the effects of measurement error and the influences of variables not included in the regression equation.
Limitations
First, a knowledge of a regression coefficient and its t-value can suggest the extent of association or influence that an independent variable has on the dependent variable. However, if an omitted variable is correlated with the independent variable, the regression coefficient will reflect the impact of the omitted variables on the dependent variables. A second limitation is that the model is based on collected data that represent certain environmental conditions. If those conditions change, the model may no longer reflect the current situations and can lead to erroneous judgments. Third, the ability of the model to predict, as reflected by r2, can become significantly reduced if the prediction is based on values of the independent variables that are extreme in comparison to the independent variable values used tc estimate the model parameters. Fourth, the model is limited by the methodology associated with the data collection, including the sample size and measures used.
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