Linked Questions

1
vote
2answers
400 views

Bivariate normal distribution , link $\Bbb E(Y\mid X=x)$ and $\Bbb E(X\mid Y=y)$ [duplicate]

Note: I edited this question on 1/1/2018 because of the comments on the original question. So some comments relate to the earlier version. It is closed as duplicaten but I dusagree with that For a ...
0
votes
0answers
66 views

Epsilon from Bivariate Normal Distribution [duplicate]

I came across the following example from a book. I am given a dataset generated from a bivariate normal distribution: Among the data, there are missing values for the last 20 of x2i (but not for x1i)....
0
votes
0answers
26 views

Proof for bivariate conditional mean of Gaussian dist [duplicate]

I see that a lot of questions are answered here for multivariate and bivariate conditional distributions. But I did not find the proof of these equations (I need just for bivariate case). to get this ...
112
votes
4answers
32k views

Assessing approximate distribution of data based on a histogram

Suppose I want to see whether my data is exponential based on a histogram (i.e. skewed to the right). Depending on how I group or bin the data, I can get wildly different histograms. One set of ...
57
votes
2answers
18k views

Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?

The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other ...
21
votes
3answers
8k views

How does the formula for generating correlated random variables work?

If we have 2 normal, uncorrelated random variables $X_1, X_2$ then we can create 2 correlated random variables with the formula $Y=\rho X_1+ \sqrt{1-\rho^2} X_2$ and then $Y$ will have a correlation ...
18
votes
4answers
699 views

What is the intuition behind the independence of $X_2-X_1$ and $X_1+X_2$, $X_i \sim N(0,1)$?

I was hoping someone could propose an argument explaining why the random variables $Y_1=X_2-X_1$ and $Y_2=X_1+X_2$, $X_i$ having the standard normal distribution, are statistically independent. The ...
15
votes
3answers
11k views

Understanding the confidence band from a polynomial regression

I'm trying to understand the result I see in my graph below. Usually, I tend to use Excel and get a linear-regression line but in the case below I'm using R and I get a polynomial regression with the ...
16
votes
5answers
3k views

Generate normally distributed random numbers with non positive-definite covariance matrix

I estimated the sample covariance matrix $C$ of a sample and get a symmetric matrix. With $C$, I would like to create $n$-variate normal distributed r.n. but therefore I need the Cholesky ...
7
votes
1answer
29k views

What do vertical bars mean in statistical distributions?

What do the vertical bars mean in the first and third formulae? $$v_i|z_i=k,\mu_k\sim\mathcal{N}(\mu_k, \sigma^2)$$ $$P(z_i=k)=\pi_k$$ $$\pi|\alpha\sim \text{Dir}(\alpha/K1_K)$$ $$\mu_k\sim H(\lambda)...
4
votes
1answer
3k views

Should the average prediction = the average value in regression?

Very basic statistics question: should the average prediction from a regression model equal the average value of the dependent variable using the same data? For example, if I collect data on the ...
10
votes
2answers
885 views

Appropriate measure to find smallest covariance matrix

In the textbook I am reading they use positive definiteness (semi-positive definiteness) to compare two covariance matrices. The idea being that if $A-B$ is pd then $B$ is smaller than $A$. But I'm ...
8
votes
3answers
6k views

Meaning of Square Root of Covariance / Precision Matrices

Say $X \in \mathbb{R}^n$ is a random variable with covariance $\Sigma \in \mathbb{R}^{n\times n}$. By definition, entries of the covariance matrix are covariances: $$ \Sigma_{ij} = Cov( X_i,X_j). $$ ...
8
votes
2answers
7k views

Conditional expectation of $X$ given $Z = X + Y$

Suppose I have two independent normal variables $X$ and $Y$ with known mean and variance. Defining $Z = X+Y$, what is the most straightforward way to compute $\mathbb{E}\left[X|Z\right]$? I am ...
5
votes
4answers
586 views

Expected value of q given y is weighted average of mean q and and y

It is assumed that: 1) $y=q+u$ Where $q$ is productivity and $y$ a testscore that measures true productivity. $u$ is a normally distributed error term, independent of $q$, with zero mean and ...

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