A brief note on variable types in multiple regression analysis: for Finance and Accounting students

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

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

The reply: "In the context of Finance and Accounting research projects using multiple regression analysis, the variable types can be understood as follows:

• Independent Variable: These are the variables that explain or predict changes in the dependent variable. They are sometimes called explanatory or predictor variables. For example, in financial analysis, earnings per share or interest rates could serve as independent variables influencing stock price.​

• Dependent Variable: This is the outcome variable that the study aims to explain or predict. In finance, it could be stock price, revenue, or firm performance measured by financial ratios. The dependent variable depends on the independent variables.​

• Controlled Variable: In regression, these are variables that researchers keep constant or statistically control to isolate the effect of independent variables on the dependent variable. For example, controlling for firm size or industry type to avoid confounding effects.

• Moderating Variable: A variable that influences the strength or direction of the relationship between an independent and dependent variable. It specifies when or for whom an effect occurs. For instance, in finance, the effect of earnings on stock price might be moderated by market sentiment or economic conditions.​

• Mediating Variable: This explains the mechanism or process through which an independent variable affects a dependent variable. It acts as a conduit or pathway. For example, in accounting research, the relationship between corporate governance and firm value might be mediated by financial transparency.​

• Exogenous Variable: Variables that are not influenced by other variables in the model but can affect endogenous variables (dependent or mediating variables). They often represent external factors or predictors determined outside the system studied. In finance, macroeconomic indicators can be exogenous variables.​

These roles help researchers structure models to accurately understand relationships and causal pathways in financial and accounting phenomena using multiple regression analysis."

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

The reply: "In multiple regression analysis, the different types of variables are located and incorporated into the regression formula as follows:

• The dependent variable (Y) is the outcome being predicted or explained. It appears on the left side of the regression equation.

• The independent variables (X1, X2, ..., Xp) are predictors or explanatory variables. They appear on the right side of the equation, each multiplied by a regression coefficient (β1, β2, ..., βp) that quantifies their effect on Y.

• Controlled variables are included as additional independent variables to account for their influence and isolate the effects of the main independent variables.

• Moderating variables are often incorporated by including an interaction term in the model, which is the product of the moderator and the independent variable (e.g., X1 * Moderator). The coefficient on this interaction term shows how the relationship between X1 and Y changes depending on the moderator's value.

• Mediating variables are included as independent variables that transmit the effect of another independent variable onto the dependent variable. Mediation analysis often involves multiple regression steps to estimate the pathways (e.g., independent variable to mediator, then mediator to dependent variable).

• Exogenous variables are predictors determined outside the model and included as independent variables affecting the dependent variable without being affected by other variables in the regression.

The multiple regression formula is generally expressed as:

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_p{X}_p+ϵ$$

where

• $Y$ is the dependent variable,

• $X_1,X_2,\mathrm{.}\mathrm{.}\mathrm{.},X_p$ are independent (including controlled, moderating, mediating, exogenous) variables,

• ${\beta }_0$ is the intercept,

• ${\beta }_1,{\beta }_2,\mathrm{.}\mathrm{.}\mathrm{.},{\beta }_p$ are regression coefficients,

• $ϵ$ is the error term.

For moderating variables, the formula is expanded with interaction terms, for example:

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2\text{Moderator}+{\beta }_3(X_1\times \text{Moderator})+ϵ$$

For mediating variables, separate regression models estimate the effect paths, typically:

1. Regress mediator on independent variable.

2. Regress dependent variable on both independent variable and mediator.

This incorporation enables researchers to examine both direct and indirect effects within finance and accounting research contexts.​

This structure allows for clear estimation and interpretation of how different variables relate within financial or accounting phenomena using multiple regression analysis."

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