In the linear model Y = BX + E, what does the symbol X represent?

In the linear model Y = BX + E, what does the symbol X represent?

• A. Y represents the outcome variable
• B. X represents the error terms
• C. X represents the predictor variables
• D. E represents the predictor variables

Answer: (C)

X represents the predictor variables—the inputs or regressors used to explain the outcome Y. In the equation, Y is modeled as a linear combination of these predictors with coefficients B, and then the random error term E is added to account for variation not captured by the predictors. If there’s more than one predictor, X is a vector (or a design matrix) of their values across observations, and B contains the corresponding coefficients that quantify how much Y changes with each predictor. This makes clear that Y is the outcome being predicted, X are the inputs used to make that prediction, and E captures the residual noise.

X represents the predictor variables—the inputs or regressors used to explain the outcome Y. In the equation, Y is modeled as a linear combination of these predictors with coefficients B, and then the random error term E is added to account for variation not captured by the predictors. If there’s more than one predictor, X is a vector (or a design matrix) of their values across observations, and B contains the corresponding coefficients that quantify how much Y changes with each predictor. This makes clear that Y is the outcome being predicted, X are the inputs used to make that prediction, and E captures the residual noise.