In simple linear regression, If Slope β1 is 0, there is Group of answer choicesno relationshippositive linear relationshipnegative linear relationship

Understanding the Slope in Linear Regression

1. Definition of Slope (β1): In simple linear regression, the slope (β1) represents the change in the dependent variable (Y) for a one-unit change in the independent variable (X).

2. Interpretation of β1 = 0: When the slope (β1) is equal to 0, it indicates that there is no change in the dependent variable (Y) regardless of changes in the independent variable (X). In other words, the line of best fit is horizontal.

3. Implication: This means that there is no relationship between the independent variable (X) and the dependent variable (Y).

4. Options Analysis:

   • No relationship: This is correct, as β1 = 0 implies that changes in X do not affect Y.
   • Positive linear relationship: Incorrect, as there is no increase in Y with increase in X.
   • Negative linear relationship: Incorrect, as there is no decrease in Y with increase in X.

Final Answer

The correct option is no relationship.