Question

Which is the correct null hypothesis for testing if the independent variable is a significant predictor of the dependent variable (i.e. has a relationship) in simple linear regression model?
A. H0: β1 = 0
B. H0: μ = 0
C. H0: rho = 0
D. H0: β0 = 0

Answer 1

Answer:

Option A) $H_0: \beta_1 = 0$

Step-by-step explanation:

The regression equation gives us a relation between the independent and the dependent variable.

The regression equation with 1 independent variable can be written as:

$y = \beta_0 + \beta_1x\\\text{where } \beta_0 \text{ is the y intercept and } \beta_0 \text{ is the coefficient of x or the independent variable.}$

• The hypothesis tells us whether the dependent variable have a significant relationship with the independent variable or not.

• We test that there is no effect of the particular dependent variable on the predicted variable.

• We carry this hypothesis with the null hypothesis that there is no significant relationship between the dependent variable and the independent variable

• Thus, we check whether the coefficient of x is zero or not.

The null hypothesis can be designed as:

$H_0: \beta_1 = 0$

• The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect).

Option A) $H_0: \beta_1 = 0$