Questions tagged [regression]

Question 1

I've been given the following function (reciprocal of 2nd order polynomial): $$f(x) = \frac{1}{ax^2+bx+c}$$ and an interval $I=[x_0, x_1]$. I need to find a 3rd order polynomial $g(x)=a^\prime x^3+b^\...

Question 2

In my AP Statistics class, the coverage of Pearson's Correlation Coefficient was pretty limited. It boiled down to "it's a measure of correlation such that $\hat{z_{y}}=rz_{x}$", and he only ...

Question 3

For a given integer $s \in \{1, \ldots, d\}$, we say that $\mathbf{X} \in \mathbb{R}^{n \times d}$ satisfies a restricted isometry property of order $s$ with constant $\delta_s(\mathbf{X}) > 0$ if $...

Question 4

I have come to learn that while multicollinearity affects the model "stability" and ability to examine individual affects, but does reduce overall model predictive power. I am interested in ...

Question 5

Note that I am performing a linear regression of a predictor variable $x_{i}$ with $i \in (1, 2 ..,m)$ on a response variable $y$ in a finite population of size $N_{t}$. Since the linear regression is ...

Question 6

The scalar target $z$ is modeled as $$f(x,y) = \underline c^T \underline b, \qquad \underline b=\begin{bmatrix} 1 \\ x \\ ln(y+d) \\ x \cdot ln(y+d) \end{bmatrix},$$ with unknown parameter $d$ and ...

Question 7

Say we perform regression with independent variable $x_1$ and dependent variable $y$, get a best fit line and compute the SSE. Then we realize that we have data for a second independent variable $x_2$ ...

Question 8

I am working on a constrained least squares sigmoid regression problem and would like to determine the Lipschitz constant of the objective function. The optimization problem is: \begin{equation} \...

Question 9

Question Let $n,m\in\mathbb{N}$ and $a:=(a_0,\cdots,a_m)^T\in\mathbb{R}^{m+1}$, then given a nonempty set $P:=\{(x_1,y_1),\cdots,(x_n,y_n)\}\subseteq\mathbb{R}^2$, find $a_*\in\mathbb{R}^{m+1}$ such ...

Question 10

All, To deduce the regression coefficient $$c=(A^T A)^{-1} A^T B $$, we assume that the minimum of the square root error $\sqrt{\sum({y_i - y_{hat})}^2}$, reduces to finding the minimum of the ...

Question 11

I have given $i=1,...,m$ linear independent unit vectors $\boldsymbol{x}_i\in\mathbb{R}^n$ with $\|\boldsymbol{x}_i\|=1$ and $n>m$. I define the matrix $\boldsymbol{X}\in\mathbb{R}^{n \times m}$, ...

Question 12

I'm trying to do a polynomial regression on a series of points $(t_i,\vec{p}_i)$, where $\vec{p}_i$ is a vector of position at time $t_i$. I wouldn't have any problems except the values of $\vec{p}_i$...

Question 13

This is a graph showcasing the lemonade sales as per temperature. Multiple data points: $(30, 90), (35, 100), (37, 110), (42, 125), (50, 140)$, etc. Now, as I have been studying the equation of a line....

Question 14

I have a set of data points looking as if they could follow a skew-normal distribution when plotted. The explicit way the data is generated is unknown, but 2 things are constant for each set {$x,y$} ...

Question 15

Suppose I run OLS on $$Z_t = \alpha_z + \beta_z \times Y_t + \varepsilon_{z, t},$$ where $\varepsilon_{z,t}$ is a Gaussian mean-zero and homoscedastic error term which is uncorrelated both with other ...

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Questions tagged [regression]

Approximating reciprocal of polynomial by polynomial on specific interval

Pearson's Correlation Coefficient with respect to $z$-scores.

Restricted isometry property inequality

Is multicollinearity a problem for optimizing the response with respect to inputs?

Correcting bias in covariance between a random variable and linear regression slopes from a finite sample

Identifiability & estimation: $d$ and $\underline c$ from $\lvert S \rvert = 6$

Add independent variable whilst performing statistical regression SSE decreases

Lipschitz Constant for Constrained Least Squares Sigmoid Regression

Efficient method for polynomial regression

Why does the minimum of monotonic square root of a function is the same as the mimimum of the function under root. [closed]

Given that $x_i \cdot r>0$, show that $u \cdot r>0$, where $u$ is the closest equiangular vector to all $x_i$.

Large error in polynomial regression with only minimal noise

Derivation for least squares regression

How to fit modified/generalized normal distributions

Prediction intervals for simple linear regression with estimated regressor

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