anyone can help? I would like to get an explanation of the statistical problem below.
suppose we have variables x1, x2 and y. all three are positively correlated. correlation x1 and y is stronger than correlation x2 and y. correlation x1 and x2 is also stronger than correlation x2 and y.
if I regress x2 to y, the result will be positive and significant.
but if I regress x1 and x2 to y, the coefficient x1 must be positively significant. but the x2 coefficient can be significant positive, can be insignificant and can also be significant negative. depending on the difference in the correlation of the three variables. how could this happen?