Tagged Questions

1
vote
0answers
38 views

Interpretation of Variance and Covariance

I am totally new to statistics and I have to create a variance and covariance analysis. I am using SPSS for this. I have created the covariance table: Hopefully it is the right thing. The first 3 ...
0
votes
0answers
22 views

calculating variance of sum of predicted costs from two-part model

I have a question regarding the calculation of the variance of the sum of predicted health care costs using a two-part regression model. Details are below, but it boils down to how to calculate the ...
0
votes
1answer
50 views

What happens to the covariance matrix when the errors are independent?

I was wondering, what happens to the covariance matrix of the errors, when I assume that all the errors are stochastically independent? Is the covariance matrix still: $$\sigma^2I = ...
0
votes
2answers
158 views

Given a table defining the joint probabilities, how do I calculate certain parameters of the marginal distributions?

The number of items sold on any one day in the traditional shop is a random variable X and the corresponding number of items sold via the Internet is a random variable Y. The joint distribution of X ...
0
votes
1answer
119 views

Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?

Let X and Y be two random variables with means $μ_X$ and $μ_Y$ , variances $σ^2_Y$, $σ^2_X$ and covariance $σ_{XY}$ . Show that $E(XY) = σ_{XY} + μ_Xμ_Y$? I tried the Covariance formula with: ...
0
votes
0answers
86 views

Covariance of binary and continuous variable

Suppose $y$ is a continuous random variable and $d$ is a binary random variable that takes the value $1$ with probability $p$ and $0$ with probability $1-p$. How do I show that ...
0
votes
0answers
214 views

Variance Covariance matrix of regression coefficients

In a procedure, I am resampling (bootstrapping) from a Y vector and X matrix. For each resample, I standardize. Then I run a linear model, and obtain the regression coefficients for each variable of ...
2
votes
0answers
54 views

Finding correlation coefficient

if I have A and B with the following known variables: with $E[A]$, $E[B]$ , $\sigma_{A}$ , $\sigma_B$ and correlation coefficient: $\rho_{AB}$ (assign numbers if you like) Say: $C=0.6A+0.4B$ Then ...
1
vote
2answers
256 views

Bounds on Cov(X, Y) given Var(X), Var(Y)?

I'm generating random multivariate normal data using the rmultnorm() function in R, which allows users to specify a vector of $k$ population means and a $k \times ...
3
votes
1answer
340 views

Covariance of a variable and a linear combination of other variables

Let $X,A,B,C,D$ be time-series variables and the covariance between any two pairs of these are known. Suppose we want to find $\textrm{cov}(X,aA + bB + cC + dD)$, where $a,b,c,d$ are constants. Is ...
2
votes
1answer
228 views

Something like Central Limit Theorem for variance and maybe even for covariance?

CLT states in short, that sum/mean of random iid variables from almost any distribution approaches normal distribution. I failed to find information about asymptotic behavior of sample variance when ...
0
votes
1answer
594 views

Mean of a product of Gaussians

If I have two normally distributed random variables, X and Y, and I want to find the mean of the distribution that results from multiplying them together, which of the following two formulas should I ...
5
votes
2answers
235 views

One component in PCA is always the mean vector in two-dimensions but not three

I've been testing PCA via SVD to decompose a simple time series data matrix, $X$. I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each ...
24
votes
6answers
7k views

How would you explain covariance to someone who understands only the mean?

...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data ...
2
votes
2answers
516 views

How to test the variance in timeseries?

I have a doubt regarding the variance, I try to explain It with an example. I have two vectors, like: ...
3
votes
1answer
133 views

Covariance and variance relation

I collected 3D velocity data in a river. the recorded timeseries of velocity components $(u,v,w)$ contains turbulent and mean part. Reynolds Shear Stress can be estimated from $$u=u'+U$$ ...