In the context of regression analysis, which of the following best describes the requirements for independent and dependent variables?

• A. The dependent variable must always be a probability value between $0$ and $1$.
• B. The independent variable must be a constant, while the dependent variable varies.
• C. Both the independent and dependent variables must be categorical.
• D. The independent variable is manipulated to observe its effect on the dependent variable, and the dependent variable is the outcome being measured.

Answer: (D)

Verified step by step guidance

1. Understand the roles of independent and dependent variables in regression analysis: the independent variable is the one that is manipulated or controlled to observe its effect, while the dependent variable is the outcome or response being measured.
2. Recognize that the dependent variable in regression analysis is not restricted to probability values between 0 and 1; it can be continuous, categorical, or other types depending on the regression model used.
3. Note that the independent variable does not have to be a constant; it typically varies to see how changes in it affect the dependent variable.
4. Acknowledge that both variables do not have to be categorical; regression can involve continuous, categorical, or mixed types of variables.
5. Conclude that the best description is that the independent variable is manipulated to observe its effect on the dependent variable, which is the outcome being measured.