In a simple linear regression model, testing whether the slope b ₁ of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation r equals zero.

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In simple linear regression, testing whether the slope (β1) is zero is equivalent to testing if there is no linear relationship between the variables, which is the same as testing if the population correlation coefficient (r) is zero. If the slope is zero, it implies that changes in the predictor variable do not predict changes in the response variable, indicating no linear correlation.

In a Simple Linear Regression Model, Testing Whether the Slope