Which of the following is NOT a component of the simple linear regression model?
A. Dependent variable (y)
B. Independent variable (x)
C. Error term (ε)
D. Regression coefficient (α)
Answer (2)
In simple linear regression, the main components include the dependent variable (y), independent variable (x), and an error term (ε). The option D, 'Regression coefficient (α)', is not a recognized component as it should refer to the slope coefficient (β) instead. Therefore, the correct choice is D.
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In a simple linear regression model, we try to determine how one variable, known as the independent variable (x), affects another variable, called the dependent variable (y). The model is typically represented by the equation:
y = β 0 + β 1 x + ε
Breaking down the components of this model:
Dependent Variable (y): This is the outcome variable that we are trying to predict or explain. It depends on the independent variable.
Independent Variable (x): This is the predictor variable that we use to predict the dependent variable.
Error Term (ε): Also known as the residual, this represents the random error in the relationship and accounts for the variability in y that x cannot explain.
Regression Coefficients ( β 0 and β 1 ): These are the parameters of the model. Specifically, β 0 is the intercept, which represents the expected value of y when x is zero, and β 1 is the slope, which indicates the change in y for a one-unit change in x.
Given these components, the option (D) 'Regression coefficient (α)' is NOT a component of the simple linear regression model, because the standard notation for regression coefficients in this context is typically β 0 for the intercept and β 1 for the slope, not α .
