In the linear model yi = β0 + β1xi + εi, εi is called the:Multiple choice question.regression coefficient.independent variable.dependent variable.error.

Break Down the Problem

1. Identify the components of the linear equation $y_i = \beta_0 + \beta_1 x_i + \epsilon_i$.
2. Determine the meaning of $\epsilon_i$ in the context of the model.

Relevant Concepts

3. In a linear regression model:
   • $y_i$ is the dependent variable (the outcome).
   • $x_i$ is the independent variable (the predictor).
   • $\beta_0$ is the y-intercept.
   • $\beta_1$ is the regression coefficient (slope).
   • $\epsilon_i$ represents the error term (the difference between observed and predicted values).

Analysis and Detail

4. The term $\epsilon_i$ captures the variation in $y$ that cannot be explained by the linear relationship with $x$. It accounts for factors not included in the model, measurement errors, or inherent randomness in the data.

Verify and Summarize

5. By reviewing the definitions:
   • Regression coefficient refers to $\beta_1$.
   • Independent variable refers to $x_i$.
   • Dependent variable refers to $y_i$.
   • Error refers to $\epsilon_i$.

Final Answer

The correct answer is error.