In a simple regression analysis for a given data set,if the null hypothesis β = 0 is rejected,then the null hypothesis ρ = 0 is also rejected.This statement is ___________ true.
A)Always
B)Never
C)Sometimes

Question

Quizplus · Accepted Answer

In a simple linear regression analysis, if the null hypothesis β = 0 is rejected, it means that there is a significant linear relationship between the dependent variable and the independent variable. As correlation coefficient ρ measures the strength and direction of the linear relationship between two variables, if there is a significant linear relationship between two variables, it is highly likely that the correlation coefficient will also be significant. Therefore, rejecting the null hypothesis β=0 implies rejecting the null hypothesis ρ=0 as well in the case of simple linear regression. Hence, the statement is always true.

In a Simple Regression Analysis for a Given Data Set,if