$cor(B_1,Y) > cor(B_2,Y) > 0$ but $cor(A + B_1, A+Y) < cor(A + B_2, A+Y)$. Is this possible? When I was processing data I came across this strange phenomenon. Say I have time series with positive values only, $A, B_1, B_2, Y.$ $\operatorname{cor}(X,Y)$ is the correlation of $X,Y.$
Here I have $\operatorname{cor}(B_1,Y) > \operatorname{cor}(B_2,Y) > 0$. I add $B_1, B_2, Y$ to $A$. But then I observe that $\operatorname{cor}(A + B_1, A+Y) < \operatorname{cor}(A + B_2, A+Y)$ . 
Is this possible? Or there are some issues in my data I need to dig? 
 A: Because correlation tells you nothing about the magnitudes of variables, you can reverse their relative order by adjusting the magnitudes suitably.
Here, for instance, is a scatterplot matrix of some $(Y, B_1, B_2)$ data:

Clearly $Y$ is more highly correlated with $B_1$ than with $B_2.$
To help us appreciate the variation in magnitudes, here are the same data shown using common scales on all axes:

The correlation coefficients between $Y$ and the $B_i$ are $0.88\gt 0.67.$
Choosing $A=Y,$ here is a scatterplot matrix of the new variables also on common scales:

Here's some detail:

The correlation coefficients between $A+Y$ and the $A+B_i$ are $0.944 \lt 0.996:$ now the latter is greater than the former, reversing the original relation. 

If you would like to experiment with similar datasets, here is the R code used to generate these, along with computations of the correlations.  Know that runif generates a specified number of iid uniform variates within the range of values specified by its second and third arguments; all arithmetic operations are vector operations (vector addition and scalar multiplication).
n <- 1e2

Y <- runif(n, 1, 2)
B.1 <- 2 * Y + runif(n, -1/2, 1/2)
B.2 <- (Y + runif(n, -1/2, 1/2)) / 10
A <- Y

cor(cbind(Y, B.1, B.2))
cor(cbind(A+Y, A+B.1, A+B.2))

