A brief note on variable types in multiple regression analysis: for MBA students

A brief note on variable types in multiple regression analysis: for MBA students (information from perplexity.ai)

My question 1: "Briefly explain the following types of variables in multiple regression analysis in the context of MBA research project works: independent variable, dependent variable, controlled variable, moderating variable, mediating variable, and exogenous variable."

The reply: "In the context of MBA research projects using multiple regression analysis, the types of variables are as follows:

• Independent variable: These are the factors or predictors manipulated or observed to see their effect on the dependent variable. They are also called explanatory or predictor variables. For example, marketing spend or price could be independent variables thought to influence sales.​

• Dependent variable: This is the outcome or variable of interest that the researcher wants to explain or predict. It responds to changes in independent variables. For example, sales revenue or stock price is a dependent variable influenced by independent variables.​

• Controlled variable: Also known as control variables, these variables are held constant or statistically accounted for to isolate the effect of independent variables on the dependent variable. They help reduce confounding effects but are not the focus. For instance, controlling for seasonality when analyzing sales [general knowledge].

• Moderating variable: This variable influences the strength or direction of the relationship between an independent and dependent variable. It moderates how much or whether the IV affects the DV. For example, gender could moderate the relationship between sleep deprivation (IV) and academic performance (DV), showing different effects for men and women.​

• Mediating variable: Also called intervening variables, these explain the process or mechanism through which the independent variable impacts the dependent variable. It is part of the causal pathway. For example, education level may mediate the relationship between age (IV) and job satisfaction (DV) by explaining why older people have higher job satisfaction.​

• Exogenous variable: In regression, this typically refers to variables that are not influenced by other variables in the model; they are independent in nature and affect other variables but are not affected themselves. They often correspond to independent variables or predictors that cause changes in dependent variables without reciprocal effects [general knowledge].

These variable types help MBA researchers design robust multiple regression models to examine complex relationships among factors influencing business outcomes."

My question 2: "How are these types of variables located and incorporated into a multiple regression formula?"

The reply: "In multiple regression analysis for MBA research projects, the different types of variables are incorporated into the multiple regression formula as follows:

• The dependent variable (DV), also called the outcome or criterion variable, is represented as $y$ in the formula. It is what you are trying to predict or explain.

• The independent variables (IVs) or predictors, which can include controlled variables, moderating variables, and exogenous variables, are represented as $X_1,X_2,\dots ,X_n$. Each IV has a corresponding coefficient ${\beta }_1,{\beta }_2,\dots ,{\beta }_n$ that measures its effect on the DV.

The general formula for multiple regression is:

$$y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_n{X}_n+ϵ$$

Here,

• $y$ is the dependent variable,

• ${\beta }_0$ is the intercept,

• $X_1,X_2,\dots ,X_n$ are independent variables,

• ${\beta }_1,{\beta }_2,\dots ,{\beta }_n$ are regression coefficients, and

• $ϵ$ is the error term.

• Controlled variables are included as independent variables in order to control for their effect while assessing the main IVs.

• A moderating variable is incorporated by including an interaction term between the moderator and the independent variable, e.g., ${\beta }_3(X_1\times M)$, where $M$ is the moderating variable. This shows how the effect of $X_1$ on $y$ changes depending on $M$.

• A mediating variable $M$ is analyzed as an intermediate variable between an IV and the DV. Mediation analysis often involves multiple regression steps: one regressing $M$ on the IVs, and another regressing $y$ on both $M$ and IVs to assess the mediation effect.

• Exogenous variables typically correspond to independent variables that influence the DV but are not affected by other variables in the model. They are represented as standard IVs without reciprocal paths in the formula.

Essentially, variable types shape how they are specified and tested in the regression model structure. Moderators add interaction terms, mediators require sequential or path analysis, while controlled and exogenous variables are included as predictors. This allows MBA researchers to capture complex relationships in their multiple regression models effectively.​

This explains the location and incorporation of each variable type in the multiple regression formula relevant to MBA research projects."

A collection of blog notes on using chatgpt for research purpose.