Hi I'm given a rather ambigious question on correlations. My question is how do we determine the correlation between 2 varibles given their correlation with other variables?
Correlation between chocolate consumption per capita and number of Nobel laureates per 10 million persons for a broader list of 90 countries = 0.45
Perfect positive association bewteen chocolate consumption and chili consumption per capita (correlation = 1)
Correlation between chili consumption per capita and nobel laureates per 10 million persons: ?
1) > 0.45
2) = 0.45
3) < 0.45
4) cannot determine
Hint: if $X$ and $Y$ have correlation $1$, there are constants $m$ and $b$ (with $m \ne 0$) such that $Y = m X + b$ with probability $1$. Relate the variance of $Y$ to the variance of $X$, and the covariance of $Y$ and $Z$ to the covariance of $X$ and $Z$, and then the correlations...