The regression coefficient is the intercept value on the y-axis of the best-fit line; the correlation coefficient describes the direction and magnitude of the relationship and is a measure of the slope of the best-fit line.
Distinguish Between r = 0 and p = 0
r = 0 means that there is no relationship between the variables; p = 0 means that there is no linear relationship between the variables.
Distinguish Between The test of the true slope, the test of the intercept, and r2 = 0
Test of the true slope using the bivariate linear regression checks whether the slope is zero using the t test. Test of intercept is found using a point prediction that uses a formula for correction; it includes a two tailed t test. The r2 value being zero means that the coefficient of determination is zero; this would interpret as the total proportion of variance of Y explained by X; this being zero means that there is no variance in Y with respect to X.