Abstract
This chapter provides an introduction to ordinary least squares (OLS) regression analysis in R. This is a technique used to explore whether one or multiple variables (the independent variable or X) can predict or explain the variation in another variable (the dependent variable or Y). OLS regression belongs to a family of techniques called generalized linear models, so the variables being examined must be measured at the ratio or interval level and have a linear relationship. The chapter also reviews how to assess model fit using regression error (the difference between the predicted and actual values of Y) and R2. While you learn these techniques in R, you will be using the Crime Survey for England and Wales data from 2013 to 2014; these data derive from a face-to-face survey that asks people about their experiences of crime during the 12 months prior to interview.
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Key Terms
- Bivariate regression
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A technique for predicting change in a dependent variable using one independent variable.
- Dependent variable ( Y )
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The variable assumed by the researcher to be influenced by one or more independent variables.
- Heteroscedasticity
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A situation in which the variances of scores on two or more variables are not equal. Heteroscedasticity violates one of the assumptions of the parametric test of statistical significance for the correlation coefficient.
- Independent variable ( X )
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A variable assumed by the researcher to have an impact on the value of the dependent variable, Y.
- Multicollinearity
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Condition in a multivariate regression model in which independent variables examined are very strongly intercorrelated. Multicollinearity leads to unstable regression coefficients.
- OLS regression
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See ordinary least squares regression analysis.
- Ordinary least squares regression analysis
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A type of regression analysis in which the sum of squared errors from the regression line is minimized.
- Percent of variance explained ( R 2 )
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A measure for evaluating how well the regression model predicts values of Y. It represents the improvement in predicting Y that the regression line provides over the mean of Y.
- Regression coefficient ( b )
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A statistic used to assess the influence of an independent variable, X, on a dependent variable, Y. The regression coefficient b is interpreted as the estimated change in Y that is associated with a one-unit change in X.
- Regression error ( e )
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The difference between the predicted value of Y and the actual value of Y.
- Regression line
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The line predicting values of Y. The line is plotted from knowledge of the Y-intercept and the regression coefficient.
- Regression model
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The hypothesized statement by the researcher of the factor or factors that define the value of the dependent variable, Y. The model is normally expressed in equation form.
- Y -intercept ( b 0 )
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The expected value of Y when X = 0. The Y-intercept is used in predicting values of Y.
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Wooditch, A., Johnson, N.J., Solymosi, R., Medina Ariza, J., Langton, S. (2021). Ordinary Least Squares Regression. In: A Beginner’s Guide to Statistics for Criminology and Criminal Justice Using R. Springer, Cham. https://doi.org/10.1007/978-3-030-50625-4_15
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DOI: https://doi.org/10.1007/978-3-030-50625-4_15
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