# Tag Info

### How should I analyze my Likert scale data?

welcome to CV! A common and relatively simple way to analyze pre-post data with small samples is a paired samples t-test. That you can do in almost any software, including Excel. That will test ...
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### Is it possible to adjust a logistic regression model when the false positive rate is too high for observations belonging to a specific category?

If your classification model is based on a certain output variable surpassing a specific boundary, then you can adjust that output variable with a certain amount such that it changes the amount of ...

### Regarding Least Angle Regression

$\newcommand{\aset}{\mathcal{A}_k}$ What you need to show is that $|\operatorname{Corr}(x_j, r_k(\alpha) - \alpha u_k)| = \frac{|\langle x_j, r_k - \alpha u_k\rangle|}{\|r_k - \alpha u_k\|}$ are ...
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### expectation value, distribution function and the central limit theorem

You don't use CLT to get this result. What is needed is a direct evaluation of the term $E[S_n^3]$. To begin with, note that for $n \geq 3$: \begin{align*} S_n^3 = (X_1 + X_2 + \cdots + X_n)^3 = \...
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### Intuition and reasoning why LASSO can only select $n$ features when $n \ll p$

I think you can understand why LASSO selects at most $n$-features intuitively if you think about the contours of $rss = |X\beta - y|_2^2$ and $l_1 = |\beta|_1$ on the parameter space $\mathbb R^p$. ...
we know, $$\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$$ $$Y = \sum_{i=1}^{n} b_iX_i$$ notice, this is a linear combination of normal random variables so, this should follow normal distribution with ... 5 votes ### Intuition and reasoning why LASSO can only select n features when n \ll p This is an excellent question, and approach to building intuition. Unfortunately, the answer is silly: your grid search doesn't include cases where b_1 or b_2 = 0: ... 5 votes Accepted ### Finding the limiting distribution of \sqrt{n} (\hat{\tau} - \tau) as n \rightarrow \infty for N(\mu, \mu^2 \tau) Whuber's comment is to the point, since it matters whether you estimate two parameters or one. Algebraically, you are correct up to and including the computation of the expected value of the negative ... 0 votes Accepted ### Data taken from survey where survey-takers self report a continous variable You say: I want to somehow correct this bias, or at least artificially modify the data so it is distributed rationally. and also: I'm going to do a multiple regression with sleep as the DV In that ... 1 vote ### Calculate the variance of \sum\limits_{i=1}^{n-1} \sum\limits_{j=i+1}^n S(X_i - X_j) for X_1,\ldots,X_n i.i.d. random variables Since the function S is symmetric about 0, if we denote S(x - y) by \phi(x, y), then the U in your question can be viewed as a (scaled) U-statistic with the kernel \phi: \begin{align*} U = ... 1 vote ### How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? E[(X-M)^2]=E[X^2]-2ME[X]+M^2\Rightarrow M=E[X] because minimum of quadradic polynomial aM^2+bM+c is at M=-b/(2a) 2 votes Accepted ### How can I deduce the probability of auto death from a death rate per billions of miles? I think you are missing some zeros here. First of all, 20,000 miles travelled in 60 years is 1.2 million, not 1.2 billion. Second, I think the assumption which is hinted at in part b) is about how ... 2 votes Accepted ### What are the degrees of freedom to consider for a G-test when some cells have expected values of 0? The contribution of cells with zero counts is zero in the G-test since each such term is evaluated as 0 in this situation. This is based on the limit of x, which is a standard calculus result. The ... 3 votes Accepted ### Showing incompleteness of density First, let's calculate E[X^2] and E[X^4]. By evaluating the integral with the given density directly, we have \begin{align} & E[X^2] = 2C\sqrt{\lambda}\int_0^\infty x^2\exp(-\lambda x^2- \... 11 votes Accepted ### Show that the sample Mean is not complete n\bar{X} \sim \mathcal{N}(-n\sigma^2/2, n\sigma^2), so its mgf is M_{n\bar{X}}(t) = \mathbb{E}[e^{tn\bar{X}}] = \exp\left[-nt\sigma^2/2 + n\sigma^2 t^2/2\right].  At $1$ we have $\mathbb{E}[\... 5 votes Accepted ### Given$r\gt 0$, how to get$\mu_r = E[|U|^r]$where$U\sim N(0,1)? It is just a matter of integration: \begin{align*} & E[|U|^r] = \int_{-\infty}^\infty |u|^r\frac{1}{\sqrt{2\pi}}e^{-u^2/2}du \\ =& 2\int_0^\infty u^r\frac{1}{\sqrt{2\pi}}e^{-u^2/2}du \\ =& ... 2 votes Accepted ### Convergence in product of sequence of random variables The following general result would come handy in deducing what the authors did above. Result1.$Let$(\Omega,\boldsymbol{\mathfrak A},\mu)$be a measure space. Let$\langle f_n\rangle_{n\in\mathbb N}...
If the $\limsup$ is less than $\epsilon$ for every positive $\epsilon$, then it's zero. It can't be, for example, $1/3,$ because you could take $\epsilon=1/4$. It can't be $0.00042,$ because you ...