# Why is the sample correlation coefficient not $1?$

A reasonable value for the sample correlation coeffcient $\rho$ between daily maximum tem- peratures and daily ice cream sales would be

$A) 0$

$B) 1$

$C) 0.7$

$D) -0.7$

I am taking intro stats for the first time and this was a question that confounded me.

I know the answer is neither $A$ nor $D$. So stuck between $B$ and $C$, I chose $B$. The correct answer was $C$ - indicating the correlation isn't that strong.

I am assuming the higher the temperature, the higher the sales? Indicating some sort of straight linear trend - strong correlation ?

## 1 Answer

If the correlation was $0.7$, then the correlation is fairly strong. It wouldn't be $1$, because that would mean there would be a direct/"perfect" relation between the two.

• How am I supposed to know "perfection" doesn't exist? – Hawk Jul 15 '13 at 4:05
• @sidht: Just because it is hot, does not mean people will necessarily purchase ice cream. An example of something that might have a coefficient correlation of $1$ is something that is directly related to the other: breathing oxygen and living, or aging (from a certain age) and growing taller is another example that might be close to $1$. – Sujaan Kunalan Jul 15 '13 at 4:12
• I apologize for my stupid comment, but i just realized people could also go out and byu cold drinks. – Hawk Jul 15 '13 at 4:16
• Don't worry. There are no stupid questions. :) – Sujaan Kunalan Jul 15 '13 at 4:19
• For your amusement. I thought the order of arranging a 10 song playlist didn't care about order because I don't listen to music... – Hawk Jul 15 '13 at 4:26