Final answer:
Adding several variables to a regression analysis primarily helps in controlling for several variables at once, which is crucial for isolating the effects of the explanatory variable and addressing lurking variables.
Step-by-step explanation:
Adding several variables to a regression analysis can help control for several variables at once. By doing this, researchers can better isolate the explanatory variable and examine its exclusive effect on the response variable, thus, not only enhancing the depth of the study but also allowing for more accurate causal inference. This method aligns with the principle of ceteris paribus, often used in experimental design, which means 'all other things being equal' to study the effect of one factor at a time on the dependent variable. This is essential to address lurking variables that may confound the results.
Therefore, the correct answer to the student's question is (b) Control for several variables at once. While increasing the construct validity and statistical significance of the results can be an outcome of adding more variables, this is not the primary purpose of doing so in regression analysis. Moreover, meeting the temporal precedence criterion for causal inference involves the sequence of events and is not directly related to the number of variables in a regression model.