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

Question

Quizplus · Accepted Answer

The correlation coefficient (ρ) between the predictor and the response variable (x and y) can be described as the square root of the R-squared value of the simple regression analysis (β). Therefore, if the null hypothesis for β is rejected, indicating a significant relationship between x and y, then the null hypothesis for ρ must also be rejected, as there is evidence to suggest a non-zero correlation between the two variables. Hence, the statement is always true.

In a Simple Regression Analysis for a Given Data Set,if β\betaβ

In a Simple Regression Analysis for a Given Data Set,if $\beta$