correlation correlation normalizes everything by the standard deviation of each attribute (just divide the covariance by the standard deviations of both variables and that normalizes thingsby doing soi can say very clearly that correlation of - means there' perfect inverse correlationso as one value increasesthe other decreasesand vice versa correlation of means there' no correlation at all between these two sets of attributes correlation of would imply perfect correlationwhere these two attributes are moving in exactly the same way as you look at different data points remembercorrelation does not imply causation just because you find very high correlation value does not mean that one of these attributes causes the other it just means there' relationship between the twoand that relationship could be caused by something completely different the only way to really determine causation is through controlled experimentwhich we'll talk about more later computing covariance and correlation in python alrightlet' get our hands dirty with covariance and correlation here with some actual python code so againyou can think conceptually of covariance as taking these multidimensional vectors of variances from the mean for each attribute and computing the angle between them as measure of the covariance the math for doing that is lot simpler than it sounds we're talking about high dimensional vectors it sounds like stephen hawking stuffbut reallyfrom mathematical standpoint it' pretty straightforward computing correlation the hard way ' going to start by doing this the hard way numpy does have method to just compute the covariance for youand we'll talk about that laterbut for now want to show that you can actually do this from first principlesnbuqmpumjcjomjof jnqpsuovnqzbtoq gspnqzmbcjnqpsu efgef@nfbo ynfbo nfbo sfuvso efgdpwbsjbodf 