What is the purpose of testing whether

₁ = 0?

The purpose of testing whether ₁ = 0 is to determine whether or not the regression line provides a good fit for the data.The purpose of testing whether ₁ = 0 is to determine whether or not there is a cause-and-effect relationship between x and y. The purpose of testing whether ₁ = 0 is to determine whether or not the mean of the x values is equal to the mean of the y values.The purpose of testing whether ₁ = 0 is to determine whether or not there is a significant relationship between x and y.

If we reject ₁ = 0, does it imply a good fit?

Rejecting ₁ = 0 does not necessarily imply a good fit. For example, if ₁ = 0 is rejected and r² is high, there is a statistically significant relationship between x and y but the fit is not very good.Rejecting ₁ = 0 never implies a good fit. If ₁ = 0 is rejected, there is not a statistically significant relationship between x and y which never implies a good fit. Rejecting ₁ = 0 always implies a good fit. If ₁ = 0 is rejected, there is a statistically significant relationship between x and y which always implies a good fit.Rejecting ₁ = 0 does not necessarily imply a good fit. For example, if ₁ = 0 is rejected and r² is low, there is a statistically significant relationship between x and y but the fit is not very good.