Question

When we conclude that β₁ = 0 in a test of hypothesis or a test for significance of regression, we can also conclude that the correlation, ρ, is equal to ______

Answer 1

$\beta _{1}=0$ indicates slope if the regression line $y=\beta _{0}+\beta _{_{1}}x$ is zero.

Slope of regression line indicates the relation between dependent and independent variables. If slope is positive there exists positive relationship between dependent and independent variables hence positive correlation exists. Similarly for negetive slope negetive correlation exists.

And for zero slope no correlation exists. Hence for zero slope the correlation $\rho =0$

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