In a simple linear regression model,testing whether the slope β₁ of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation ρ equals zero.

Question

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Testing whether the slope (β1) of the population regression line is zero is equivalent to testing if there is no linear relationship between the two variables, which is the same as testing if the population coefficient of correlation (ρ) equals zero, since ρ measures the strength and direction of a linear relationship between two variables.

In a Simple Linear Regression Model,testing Whether the Slope β1

In a Simple Linear Regression Model,testing Whether the Slope β₁