In a simple linear regression model, testing whether the slope, $\beta _ { 1 }$ , of the population regression line is zero is the same as testing whether the population coefficient of correlation, $\rho$ , equals zero.

Question

Quizplus · Accepted Answer

In simple linear regression, the slope $\beta_1$ is directly related to the correlation coefficient $\rho$. If $\beta_1 = 0$, it implies no linear relationship, which means $\rho = 0$.

In a Simple Linear Regression Model, Testing Whether the Slope β1\beta _ { 1 }β1​

In a Simple Linear Regression Model, Testing Whether the Slope $\beta _ { 1 }$