Final answer:
To reduce the list of potential predictor variables, draw scatter plots, calculate the least-squares line and correlation coefficient, check for outliers, and use statistical criteria such as adjusted R-squared to evaluate each variable's contribution to the model, with Option C being a good method.
Step-by-step explanation:
When compiling a comprehensive list of potential predictor variables for a regression model, it can be overwhelming to deal with a large number of variables. Reducing the list to a manageable size while still capturing the important information can be accomplished through several techniques:
- Understand the relationship between the variables by deciding which variable should be the independent variable and which should be the dependent variable. Then, draw a scatter plot of the data to visually inspect if there is a relationship.
- Calculate the least-squares line and place the equation in the form ý = a + bx to see how the dependent variable changes with the independent variable.
- Examine the correlation coefficient to understand the strength and direction of the linear relationship between the variables. If this coefficient is significant, it adds evidence that the variable should be included in the model.
- Assess whether a linear relationship is suitable by observing the scatter plot, the fit of the least-squares line, and the presence of any outliers that may influence the regression disproportionately.
- Consider using statistical criteria like the adjusted R-squared, which adjusts for the number of predictors in the model, to determine the contribution of each variable while penalizing for adding too much complexity.
In summary, Option C, 'Use the adjusted R2 criterion to reduce the list' is a good method to consider for reducing the list of predictor variables in regression analysis. It helps in maintaining a balance between the complexity of the model and its predictive power.