# Tagged Questions

Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.

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### Matrix Regression help for exam revision

My regression exam is a month away and i am trying to learn Matrix regression however and struggling with the questions as a whole they are: (a) Consider two independent random variables ξ1 and ξ2, ...
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### Geometrical Properties of a curve in 3D

I have $n$ curves in the 3d space, which I represented with a certain amount of points. (That is, for every curve $i$, there is a vector $v_i$ with $m$ points which belong to the curve) My goal is to ...
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### Non-Linear Model Transformation

I want to transform this Non-Linear Model $y= 8-ae^{bx}$ to Linear.And my issue is in this step $lny=ln(8-ae^{bx})$ how can simplify it to reach in a linear model which is like this $y*=b0+b1x$ ...
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### Likelihood of an autoregressive model

I have the following autoregressive model: $Y_I=\lambda_t + \alpha_t(Y_t-\lambda_{t-1}) + \epsilon_t$ where $\lambda_t=\beta_1+\beta_2cos(\pi t/6)+\beta_3sin(\pi t/6)$ and $\epsilon$ has a ...
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### Retrieve inputs for second pass (cross section) regression from Time series linear regression

I will explain my question through simple example best demonstrating the issue. Basically I work with Matlab, so if there is already implemented lib functions for this - That's can be the answer. And ...
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### Regression: Service time based on number of copiers

For a random sample of 10 service calls, both the number of copiers and the total service time were recorded. Number of Copiers (x) : 4, 2, 5, 7, 1, 3, 4, 5, 2, 6 ...
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### Prove information matrix equality for binary Logit model

I need to prove the information matrix equality for a binary logit model. I know that in general the information matrix equality means the following: "The Information Matrix Equality (IME), which is ...
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### Calculated product of two projection matrices

how do i show that $$P_MP_m=P_mP_M=P_m$$ where $$P_M=X_M(X'_MX_M)^{-1}X'_M$$ $$P_M=X_m(X'_mX_m)^{-1}X'_m$$ and $X_m$ is embedded into the larger matrix with the same number of columns $X_M$.
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### given a set of points and vectors, expand the set

I have a set of $n$ points: $(Sx, Sy, Sz)$ and $n$ vectors: $(Vx,Vy,Vz)$, each uniquely mapped to one another. The set also exists inside of an $X*Y*Z$ size rectangular space. I want to ensure a ...
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### Parameterizing conditional expectations in terms of regression coefficients (gaussian case)

Consider three jointly normally distributed random variables $X,Y$ and $Z$. I know that in the Gaussian case $$E[Z\mid X, Y]=\beta_{ZX;Y}X +\beta_{ZY;X} Y$$ where $\beta_{ZX;Y}$ notes the ...
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### using simple regression to capture a “normal range” for a dependent variable against a factor?

The question reads as follows My JMP output of the simple regression of the data is as follows: Is this all I need? The question phrasing is somewhat throwing me for a loop. Is there something ...
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### Simple Regression ~ House Price Prediction

I am stuck with this question. "You have a data set consisting of the sales prices of houses in your neighborhood, with each sale time-stamped by the month and year in which the house sold. You ...
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### What does it mean to regress out current features?

First of all, I'd like to say that this is the intro to a homework problem. Please do not post any answers, I am only looking for clarification on some terminology in the setup. I am trying to ...
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### How to regress certain non-linear data

How can I perform a regression onto data of that follows this shape: $$U(x):=\sum_{i=1}^N\, a_ix^ie^{-b_ix}$$ where the $a_i\in \mathbb{R}$ and the $b_i \in (0,\infty)$ ...
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### How to fit sum of products of sine waves?

System Model: \begin{align} Y(t_1, t_2, t_3) = A \bigg[ & 2+ k_1\cos(w_1t_1+\phi_1) +k_2\cos\left(w_2t_2+\phi_2\right)+ \\[2ex] &4k_3\cos\left(\dfrac{w_1t_1+\phi_1}{2}\right)\cos\left(\dfrac{...
### Compute linear regression slope over $[x_i, y_i]$ when $x_i$ samples over $x$ are regularly distributed.
Context: To have an idea of the trend-line of a set of samples $[x_i, y_i]$, I usually compute the slope $a$ in the linear regression ($y = ax + b$) with a spreadsheet software and the formula:  a ...
### Power Regression $y=Ax^B+C$
I have to do reproduce a power regression but I don't have any experience in procedures like that. I read a little bit about power fit/power regression and that a formula like $y = ax^b$ is used for ...