In order to determine whether the coefficient in a simple linear regression model is significant or not, which null hypothesis do we propose?β0=0β0≠0β1=0β1≠0

To determine whether the coefficient in a simple linear regression model is significant, we specifically test the significance of the slope coefficient, often denoted as $\beta_1$. The null hypothesis typically states that the slope is equal to zero, which implies that there is no relationship between the independent variable and the dependent variable.

Null Hypothesis

1. $H_0: \beta_1 = 0$ - This means that changes in the independent variable do not affect the dependent variable; there is no significant relationship.

Alternative Hypothesis

2. $H_a: \beta_1 \neq 0$ - This suggests that changes in the independent variable do have an effect on the dependent variable, indicating a significant relationship.

Thus, the correct answer is:

$\beta_1 = 0$.