# Tag Info

3

In the notation you quote from this paper $r$ is the sample correlation; it estimates the population correlation $\rho.$ $N$ is the number of $(x,y)$-pairs upon which the test is based. Many texts would use $n$ because this is a sample. This is a test of $H_0: \rho = 0$ against $H_1: \rho \ne 0$. Under the assumption that $H_0$ is true and that the data ...

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This probably belongs on CrossValidated. It seems like a reasonable question but not quite as easy as you might like to answer (without shortcuts). A statistician's model of this would probably start with a Poisson-distributed response (reasonable for count data). It is most straightforward to assume that posting has an effect on the log-density of the ...

2

If we ae told that $X$ and $Y$ are jointly Normal, then we know that $$E[X|Y] = E[X] + \rho \frac{\sigma_X}{\sigma_Y}( Y-E[Y])$$ in which in your case reduces to $$E[X|Y] = \rho Y$$ In general, if we only know that the variables are marginally Normal, then I don't think there's much to say. Calling $E[X|Y]=g(Y)$ we know that write $$E[XY] = E[E[XY|Y]] ... 1 You should prove: that E[X_t] is a number independant of t, say \mu. that the autocovariance E[(X_t-\mu)(X_{t+h}-\mu)] is only a function of h (the lag) and not t. If X_t is a one-dimensional stochastic process, then the autocovariance and autocorrelation functions are also one-dimensionnal. Otherwise, these are matrix with the same ... 1 If your data x_1, \dots, x_n have mean 0 (and the y values satisfy this as well) then R and C are equal. The coefficient you define as C should always be used as Pearson's r (a.k.a. the correlation coefficient), but in the specific case where x, y have 0 means you can use the simpler formula R, since C = R in this case. 1 First, your random process X[n], n \in \mathbb{N} is collection of infinitely many random variables X[1],X[2],\ldots; if we take finitely many of them, say, X[1],\ldots,X[n] and form random vector$$X=(X[1],\ldots,X[n]) this random vector is sometimes called a finite-dimensional section of random process $X[n], n \in \mathbb{N}$. With every random ...

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