In simple linear regression, rejecting the $\beta$= 0 null hypothesis in the key hypothesis test means:
A)we haven't yet found sufficient sample evidence that there's a useful linear relationship between x and y.
B)we have sufficient sample evidence that there's no useful linear relationship between x and y.
C)there is convincing sample evidence of a useful linear relationship between x and y.
D)the sum of the residuals is such that no linear relationship can be established between x and y.
E)that the p-value is greater than alpha.

Question

Quizplus · Accepted Answer

Rejecting the null hypothesis in the context of simple linear regression, where the null hypothesis typically states that the slope of the regression line (β1) is equal to zero, indicates that there is statistically significant evidence to suggest that there is a non-zero slope. This implies a linear relationship between the independent variable (x) and the dependent variable (y), thus providing convincing sample evidence of a useful linear relationship between x and y.

In Simple Linear Regression, Rejecting The β\betaβ = 0 Null Hypothesis in the Key Hypothesis Test Means

In Simple Linear Regression, Rejecting The $\beta$ = 0 Null Hypothesis in the Key Hypothesis Test Means