When a logistic regression is being fit to a set of data, what is the actual value that is being maximized? What I mean is, as the coefficients are being determined, what criterion is being used to determine the "best fitting model"?  Is it: the number of cases that are correctly classified based on the calculated Y value for each case?  Thanks!
I'm trying to understand the derivation of the equations for the logistic regression. I'm following the cs229 notes:    At some point in the derivation, in the notes we need to maximize the log-likelihood of the parameters:  ℓ(θ) = log L(θ) = y log h(x) + (1 - y) log(1-h(x))  In the notes, after the derivation we get:  $\frac{\partial}{\partial \theta_j}$ = (y $\frac 1 {h(x)}$ - (1 - y) $\frac 1 {1 - h(x)}$) $\frac{\partial}{\partial \theta_j}$h(x)  Shouldn't this be:  $\frac{\partial}{\partial \theta_j}$ = (y $\frac 1 {h(x)}$ + (1 - y) $\frac 1 {1 - h(x)}$) $\frac{\partial}{\partial \theta_j}$h(x)  I've been looking at this for a while and I can't see where this minus sign is coming from...  Thanks for your help!
Can people PLEASE spell out their slang acronyms Why is it true that "I before E, except after C"? I almost hesitate to ask this, because it is hard to believe no one else asked it; but it isn't showing up in the "similar titles" list.  What is special about 'C' that switches the 'IE' immediately following it? How do I know when to use "the" versus "a" versus "∅" as an article on a noun? With proper nouns, we don't use the except for river names, newspaper names, etc.  I want to know why we use the with White House. I mean, under which rule can we categorize it? What could other similar examples for that rule be? I'm using Ubuntu 11.04 and I want to free up some space in my root directory, which is overloaded. I especially want to change the path used for installing applications (they are getting installed directly to the root drive).  Another consideration is that I'm working on a MySQL database server. The server is installed in the root directory itself, so I don't want to  risk losing any data.  Please give me some tips to help sort out this problem. Setting background-image using jQuery CSS property Applying MVT and IVT (?) to show something about f'''? (edit: actually, Taylor's Theorem using Lagrange remainder) I believe that the correct answer to this question will involve applying both the Mean Value Theorem and the Intermediate Value Theorem, perhaps several times.  However, I can't see how to proceed.  I went down what I thought were the typical paths and just reached dead ends.  Does someone maybe have a hint?  I think that with the appropriate nudge I should be able to solve this question.  If not, I'll edit and ask if someone knows how to solve the whole thing.  Here's the question:  Let $f: \mathbf R \to \mathbf R$ be such that $f$, $f'$, $f''$, and $f'''$ exist and are continuous on $\mathbf R$ and satisfying $f(-3)=-1$, $f(0)=0=f'(0)$, and $f(3)=8$.  Prove that there exists $\xi \in (-3, 3)$ such that $f'''(\xi) \ge 1$. Academic rank equivalence between the UK and the US systems I want to split a long equation in many lines I have a long line in equation. I want to split it properly in two or three lines. I've been using \begin{split} and \end{split}, but still it is not in good position. The equation's code is below.  \begin{equation} \begin{split} \frac{r(r-1)c_{0}}{z} + \\ &amp;  \sum_{0}^{\infty}[[(j+r)(j+r+1)c_{j+1} - [(j+r)(j+r-1) - l(l+1)]c_{j}] \\ &amp;= 0, \end{split} \end{equation} Let $\psi: C([0,1]; \mathbb{R}) \mapsto C([0,1]; \mathbb{R})  $, be such that if $x \in [0,1]$ then $$\psi(f)(x) = \int\limits_{0}^{x} f(t) dt $$  I am asked to show that $\psi$ is not a contraction but $\psi^{2}$ is. And then conclude that $\psi$ has a unique fixed point.   I´ve managed to prove a statment that helps me conclude the last part but I´m having trouble proving that the function is not a contraction. This is what I've got.   If $f,g \in  C([0,1]; \mathbb{R})$  then $$ |\psi (f) - \psi(g)| \leq \int\limits_{0}^{x} |f(t)-g(t)| dt \leq \sup\limits_{x\in [0,1]} |f(x)-g(x)| \int\limits_{0}^{x} 1 dt = d(f,g) x  $$ Then $|\psi (f) - \psi(g)| \leq d(f,g) x $,  and taking supremum on the left hand side allows me to conclude that $d(\psi (f),\psi (g)) \leq d(f,g) x$  Is there any problem with this procedure? Does anybody has an insight on how to procede with the $\psi^{2}$ part?   Many Thanks! Inequality : $\sum_{k=1}^n x_k\cdot \sum_{k=1}^n \frac{1}{x_k} \geq n^2$ I have to show the inequality of $$\left(\sum_{i=1}^n x_i\right)*\left(\sum_{i=1}^n \frac{1}{x_i}\right) \geq n^2.$$For $x_1, ... x_n \in \mathbb{R_{&gt;0}}$ and $ n \geq 1$. I wanted to show this inequality by induction. The basis is clear, but I am not sure how to do the inductive step. Can someone help me with that? Why does the degree of freedom of SSR equals 1 in simple linear regression How to remove shortcut key for Unity , which is "Meta" key on keyboard Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$ How to show that a set of discontinuous points of an increasing function is at most countable I would like to prove the following:       Let $g$ be a monotone increasing function on $[0,1]$. Then the set of points where $g$ is not continuous is at most countable.     My attempt:    Let $g(x^-)~,g(x^+)$ denote the left and right hand limits of $g$ respectively. Let $A$ be the set of points where $g$ is not continuous. Then for any $x\in A$, there is a rational, say, $f(x)$ such that $g(x^-)\lt f(x)\lt g(x^+)$. For $x_1\lt x_2$, we have that $g(x_1^+)\leq g(x_2^-)$. Thus $f(x_1)\neq f(x_2)$ if $x_1\neq x_2$. This shows an injection between $A$ and a subset of the rationals. Since the rationals are countable, $A$ is countable, being a subset of a countable set.    Is my work okay? Are there better/cleaner ways of approaching it? Let he who believes in this prophet speak now what he knows.       Let him who believes in this prophet speak now what he knows. Why does pdfTeX hang on this file? Windows 10 non-persistent installation (live ISO) We've got a Windows 10 installation running in an environment where it can occasionally lose power and restart. However, this sometimes leads to corruption of files.  I've had a look at Windows "To-Go" but this seems to be persistent. And I've also checked out virtualisation, but that would require us to run a non-persistent Windows 10, in another Windows 10 environment.  Is it possible to install Windows 10 as a "non-persistent live CD"? So that a user will have a seemingly fresh Windows 10, but doesn't require to re-install it at each startup? According to Ohm's Law, if the resistance is zero, the power dissipated by a resistor is unmeaning.  $$P_d = R \times I^2$$  $$I = \sqrt{ \frac {P_d}{R} }$$  Can one calculate the resistance given that power is defined? Only by knowing power, how can one calculate the maximum current of a zero-Ohm resistor?   I'm a bit confused as I've seen there is zero-Ohm resistors with specified power in the market. Can I use a present-tense verb when writing about a past event? How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions If $n$ is an integer and $n&gt;2$, then $$\bar{z}=z^{n-1}$$ has $n+1$ solutions. Does this have something to do with the rational root theorem?