Question

Q. 20

In a simple linear regression, when testing H0: β1 = 0, against H1: β1 ≠0, failing to reject the null hypothesis means that:

a. the slope of the regression line is not zero

b. the relationship between x and y may be multiplicative

c. there is no linear relationship between x and y

d. there is a linear relationship between x and y

e. None of the above

Answer 1

$H_o: \beta_1 = 0$

$H_1: \beta_1 \ne 0$

The value of slope in a linear regression determines the extent of linear relationship between x and y

Failing to reject the null hypothesis means that there is not sufficient evidence to indicate that the slope is significantly different from zero.

Hence, failing to reject the null hypothesis means that there is no linear relationship between x and y

Therefore, option-C is the correct answer.