In a simple regression analysis for a given data set,if the null hypothesis H₀: $\beta _ { 1 }$
= 0 is rejected,then the null hypothesis H₀: $\rho$
= 0 is _____ rejected.

Question

In a simple regression analysis for a given data set,if the null hypothesis H₀:

\beta _ { 1 }

= 0 is rejected,then the null hypothesis H₀:

\rho

= 0 is _____ rejected.

Quizplus · Accepted Answer

Rejecting the null hypothesis that $\beta_1 = 0$ in a simple regression analysis implies that there is a statistically significant linear relationship between the independent variable and the dependent variable. This directly implies that the correlation coefficient ($\rho$) between these two variables is not zero, because $\beta_1$ represents the slope of the regression line, and if it is not zero, it means there is a linear relationship, hence the correlation ($\rho$) is also not zero.

In a Simple Regression Analysis for a Given Data Set,if β1\beta _ { 1 }β1​

In a Simple Regression Analysis for a Given Data Set,if $\beta _ { 1 }$