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, $$P$$ , equals zero.

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In simple linear regression, the slope ($$\beta_1$$) indicates the strength and direction of the relationship between the independent and dependent variables. If $$\beta_1$$ is zero, it implies no linear relationship, which corresponds to a correlation coefficient ($$P$$) of zero.

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

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