What distinguishes simple regression from multiple regression?

What distinguishes simple regression from multiple regression?

• A. Simple regression uses multiple predictors
• B. Simple regression cannot predict
• C. Simple regression uses only the intercept
• D. Simple regression has one predictor; multiple regression has many predictors

Answer: (D)

The main idea is how many predictors are involved. In simple regression you model the outcome using a single predictor, yielding a straight-line relationship Y = β0 + β1X + ε. In multiple regression you bring in several predictors, Y = β0 + β1X1 + β2X2 + ... + βkXk + ε, to estimate the separate effect of each predictor while accounting for the others. So the defining difference is the number of predictor variables: one in simple regression, many in multiple regression. This matters because adding more predictors can improve prediction and reveal the unique contribution of each factor, but it also adds complexity and potential issues like multicollinearity.

The main idea is how many predictors are involved. In simple regression you model the outcome using a single predictor, yielding a straight-line relationship Y = β0 + β1X + ε. In multiple regression you bring in several predictors, Y = β0 + β1X1 + β2X2 + ... + βkXk + ε, to estimate the separate effect of each predictor while accounting for the others. So the defining difference is the number of predictor variables: one in simple regression, many in multiple regression. This matters because adding more predictors can improve prediction and reveal the unique contribution of each factor, but it also adds complexity and potential issues like multicollinearity.