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That r value is the key here
usually when it's this high (regardless of the critical value), it implies there's a strong correlation between the two variables
Oh, yes - I do remember learning that.
a strong correlation corresponds to the two variables being linked (one is independent and the other is dependent on that independent variable)
Makes sense, so far.
so they can't be independent if they are linked like this
that's why the claim that they are independent is rejected
Oh, I think I see what you're meaning - because the correlation (relationship) between "x" and "y" is so strong, both variables are dependent on each other, so it is not possible that they could be independent of each other?
that is close, it's more like "one variable dictates what the other variable is...so one variable is independent while the other depends on the first variable"
but yes, they are linked in a way that they can't be independent of each other
So, if the problem IS correct to have rejected the claim, what part of the problem is incorrect?
I'm not sure what you mean
oh i know what you're asking
Well, the instructions for the problem say it is false. I'm supposed to explain why it's false.
this is a very dangerous part of statistics because students often confuse correlation and causation
this is very important not to mix the two
if two variables are strongly correlated with each other, it doesn't necessarily mean that one causes the other
I should probably let you know that the last part of the problem says: NOTE: While this specific r-value is made up, this general pattern has been shown in several real world data sets involving ice cream sales and number of car wrecks in major cities on the east coast of the United States.
ie correlation does NOT imply causation
I'm not sure if the NOTE is true or false (I don't know if my professor is saying that this part is false or true.
just because they both tend to decrease (for instance), doesn't mean that one causes the other to decrease as it decreases
does that make sense?
Yes! Thank you so much! I really appreciate that you took your time to help me! :) I understand it.