Is a flat scatter plot no correlation?

is A "no correlation or zero correlation?" if so, does A have more information than B despite both showing no correlation? Because here no correlation on A means you can still predict that if you increase X, Y will stay the same.

A)

B)

1 Answer

Do not confuse slope with correlation.

Below I use R to generate data with a strong positive correlation between $X$ and $Y,$ and with a graph that looks somewhat like your (A).

set.seed(828) # for reproducibility
x = runif(20)
y = 10 + 3*x + rnorm(20,0,.5)
plot(x,y, ylim=c(0,30), pch=20)
cor(x,y)
[1] 0.8411499

Correlation has no units, so you should not expect a highly positive correlation to give the appearance of a highly positive slope on a graph.

Here is another plot of exactly the same data in which the slope appears to be greater because of the vertical scale used.