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In regression analysis, the key requirement is that independent variables can take on either categorical or continuous forms, while the dependent variable must typically be continuous. This is crucial because regression aims to model the relationship between the independent variables (explanatory variables) and a dependent variable (response variable).

When the independent variables are used to predict outcomes, it is essential that the dependent variable is continuous, allowing for precise predictions of numeric values. This aligns with standard practices in regression analysis, where techniques like linear regression specifically anticipate a continuous dependent variable to derive a numerical relationship.

Categorical independent variables are common, especially when using techniques like dummy coding to include them in the regression model. They allow for the incorporation of qualitative data, making the model versatile in handling various types of data.

In contrast, the requirements specified in the other options do not align with the fundamental principles of regression analysis. For instance, suggesting that dependent variables can be categorical is inconsistent with traditional regression; while there are alternatives like logistic regression for binary dependent variables, this does not fit within the standard linear regression framework typically discussed in this context. Each variable's type influences the type of statistical methods that can be appropriately and accurately applied. Thus, understanding these foundational principles greatly aids in correctly applying