In a simple linear regression model,testing whether the slope $\beta _ { 1 }$
of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

Question

In a simple linear regression model,testing whether the slope $\beta _ { 1 }$ 
of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

Quizplus · Accepted Answer

Testing whether the slope $\beta_1$ is zero is equivalent to testing if there is a significant linear relationship between X and Y, as a zero slope indicates no linear relationship.

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

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