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1
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
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4
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.
