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

learn more… | top users | synonyms

0
votes
1answer
28 views

How to interpret b in $y=x^{e^{bz}}$ in nonlinear regression?

What is the correct way to interpret b in this nonlinear equation $y=x^{e^{bz}}$? I've estimated the model and b seems to be the percent change in y with a unit change in z, but I am unsure how to ...
0
votes
0answers
8 views

Hosmer–Lemeshow test - Best Model

I have 3 different models and I do the Hosmer–Lemeshow test. I have a p-value and a Chi2 value. How can I know which model fits the best my data? Khi-2 || Pr > Khi-2 12.04 || 0.19 ...
0
votes
0answers
9 views

Why can I plug the roots of a partial derivative of a linear optimization objective E into E without changing it?

As an example, to fit a line to 2D data $\boldsymbol x_i$ with the parameters $\theta = (a\;\;b\;\;c)^T$ with the normal equation $\langle \boldsymbol x, ...
0
votes
0answers
31 views

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] ...
0
votes
0answers
13 views

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 ...
0
votes
0answers
42 views

Kalman Filter and OLS Results Are Different

I read that Kalman Filters can be used for continuous / online linear regression and at the end of the regression its results and ordinary linear regression (OLS) results would be the same. I tried it ...
0
votes
1answer
29 views

Simplification of a product of three matrices

Define $$\mathbf{c}_t = \begin{bmatrix} x_{1t} \\ x_{2t} \\ \vdots \\ x_{Nt} \end{bmatrix}\in \mathbb{R}^N$$ where all entries are in $\mathbb{R}$, $t = 1, 2, \dots, p+1$. I am trying to simplify ...
0
votes
2answers
42 views

Linear regression using gradient descent: is the whole weight vector updated with the same number?

I'm using gradient descent with mean squared error as error function to do linear regression. Take a look at the equations first. As you can see in eq.1, the prediction is done with a bias term b ...
0
votes
0answers
21 views

Variance in the sum of batch-correlated residuals in a regression

I am looking at a regression model of the following form: $Y=intercept+\beta_{Yf.n}X_f+\beta_{Yn.f}X_n +error$ where $X_f$ and $X_n$ are predictors. A value for $Y$ will be sampled from the ...
0
votes
0answers
14 views

Interpretation of diagonal detail in Haar Wavelet Transforms

I am a statistics grad student, and I have just begun exploring the topic of wavelet regression (specifically, Haar wavelets for discrete functions). I understand the generalization from a one ...
0
votes
0answers
20 views

Relationship/correlation between data - does it exist?

Data I refer to in this question Some analysis has been conducted for my business by an external company. The data, as it stands, only really tells part of the story and doesn't provide any real ...
0
votes
2answers
37 views

exponential regression for bacteria growth

I'm studying regression lines and curves, and I've learn the methods for working with curves of the types $ax^2+bx+c$ and $ax+b$ as well as $a\sin(x)+b\cos(x)$. Now I'm asked this: $$(0,32), ...
0
votes
1answer
41 views

How do you calculate the correlation between the intercept's and beta's standard error in a univariate linear regression?

I am running a regression to predict a variable Y as follows: $Y=\alpha+\beta\times x+\epsilon$ I am trying to get a distribution of the expected value of Y given standard errors in the model ...
0
votes
0answers
26 views

Using least squares regression to apply nonlinear function to time series data

If you have a nonlinear function (see example), can you use a least squares regression approach to fit it to time series data ? Is this approach also valid for n variables? How many time points are ...
0
votes
0answers
14 views

Predict the probabilty of a value belonging to a particular class

I have got two classes : BG and FG and a set of values assigned to each of these classes. Given a new value how can I find ...
0
votes
0answers
62 views

Help Determining Gradient for Equation

I am writing an OO program with geometric objects. My Plane object is capable of taking a collection of 3d points and determining the plane of best fit. I'm using this popular document on it from ...
0
votes
1answer
13 views

Statistic test for comparing two regression models

I'm having two linear regression models as follows: $y = a_1x_1 + a_2x_2 + c$ and $y = b_1x_1 + b_2x_3 + c$. I'm looking for a statistical test for proving which model is better. I've obtained the ...
0
votes
0answers
19 views

Categorical vs Numerical covariate linear regression

We have started doing regression at my university, and I would like to model ACT scores of students given some covariates. My problem is I have a covariate grade with values "A", "B", "C",and "F". ...
0
votes
0answers
9 views

FWL Theorem: Regressing $X_1$ on $X_2$ (a matrix on a matrix)

I am confused regarding the FWL theorem. One step is to regress $X_1$ on $X_2$ **to get the residuals from this regression*. Note that $X_i = (Txk_i)$ matrix. $k_1$ not necessarily equal to $k_2$. ...
0
votes
0answers
23 views

Rewriting residuals transposed times estimates with Annihilator and Projection: $e'\hat{y} +0 = y'M_xP_xy =0$

I am looking at a proof that says $$e'\hat{y} +0 = y'M_xP_xy =0$$ where $P_x$ is the projection matrix, $M_x$ is annihilator. I don't see how they obtain this result. What I am wondering is they are ...
0
votes
0answers
24 views

How to scale set of numbers

I have set of numbers. Set can have very big numbers (1E+13) and small (1). I need to scale numbers to range from 1 to 500. The scale should save original proportions. Table below shows that formula ...
0
votes
0answers
22 views

Neural network for regression

The way I understand regression for neural networks is weights being added to each x-input from the dataset. I want something slightly different. I want weights ...
0
votes
0answers
16 views

estimating $\sigma$ of regression based on Brownian motion

Suppose I have a regression that looks like this: $x_t = \alpha + \beta t + \sigma W_t$. Also suppose, I want to estimate $\beta$ and $\alpha$ using say $n$ discrete observations by a regression. ...
0
votes
1answer
51 views

How to calculate the linear regression model of function $y=\alpha + \beta k + \beta x$?

I have a linear function $y=\alpha + \beta k + \beta x$ and observation data that consist of pairs of $x$ and $y$. $\alpha$, $\beta$, and $k$ are unknown parameters. I want to estimate the value of ...
0
votes
0answers
34 views

Estimated simple linear regression model

Consider the simple linear regression model $y=50 + 10x + \varepsilon$ where $\varepsilon$ is $NID (0,16)$. Suppose that $n=20$ pairs of observations are used to fit this model. Generate $500$ samples ...
0
votes
1answer
36 views

Computing vector linear regression

In eye tracking we have to compute the linear regression for pupil and gaze. The formula is: $$\begin{bmatrix} gaze_x \\ gaze_y \end{bmatrix} = \begin{bmatrix} \theta_1 \\ \theta_2 \end{bmatrix} + ...
0
votes
0answers
58 views

Implementation of the LOWESS-algorithim (local regression data smoothing)

I need to implement the LOWESS-algorithm in a piece of software I am working on. The LOWESS-algorithm is a type of filter, which applies a locally weighted regression on each data point. In this ...
0
votes
0answers
29 views

Most sensitive variable

I have a question in my homework that says identify the most sensitive variable from the regression model, I have 3 dependent variables and one independent. I have found the regression equation and ...
0
votes
0answers
31 views

Combining variances

I have the following problem: I have a data file that contains monthly returns for several companies, returns of a local index and a global index. Now I want to run the following three regressions for ...
0
votes
0answers
17 views

Challenge and Interesting point - GLM for Poisson Regression for Titanic survival data

I have a professor who made a very good point about the data titanic analysis during a lecture this week. I am still however trying to better understand. He argued that it is also possible to have a ...
0
votes
0answers
12 views

Is the weighted mean of residuals over another variable equal to $0$?

I understand how residual errors must sum to zero around in a random sample (e.g. $y$-axis price of diamond predicted by x-axis weight of diamond). However, why must the weighted sum of residuals with ...
0
votes
0answers
22 views

LARS algorithm for LASSO

I see that Prof Xiaohui Chen has released his code on his website for LARS in constrained form. Does anyone know that how to solve LASSO using LARS in penalized form? To be frank, I am very new to ...
0
votes
0answers
10 views

Data transformations for optimal regression maximization and minimization

I am looking for a method/algorithm that can determine the percentage at each data-point of a specific depended variable y, that simultaneously maximizes the coefficient of determination of linear ...
0
votes
0answers
18 views

Auto covariance for AR, MA, ARMA

I think that for AR processes, ACF would alternating signs when we have something like this: $$x_t = -x_{t-1}+z_t$$ but what if we have AR(4): $$x_t = -x_{t-1}+x_{t-2}+x_{t-3}-x_{t-4}+z_t$$ based on ...
0
votes
0answers
43 views

What is the matrix $\boldsymbol X$ in $\boldsymbol X' \cdot \boldsymbol X \cdot \vec{\hat{\beta}} = \boldsymbol X' \vec{y}$?

I was trying to understand multilinear regression, and I was at the part where we use the least squares method to estimate $\vec{\beta}$. In this method, we find partial derivatives, and at the end we ...
0
votes
1answer
36 views

Linear, quadratic and exponential regression

I know the formulas for linear and quadratic regression. Please tell me 1) how to model an equation for exponential regression? 2) if I can use the gradient-point formula for linear regression and ...
0
votes
0answers
12 views

Combining predicted responses from two regressions

I am trying to find info related to combining confidence levels & intervals on predicted response variables. To explain my problem, considering the following: A and B are two different values ...
0
votes
0answers
17 views

Logistic Regression with some other Sigmoid function

I have been using Logistic regression with Newton's method where the update rule is the following: $$ W^\intercal = W^\intercal + (X^\intercal P (I - P) X)^{-1} X^\intercal(y - p) $$ Here $P$ is ...
0
votes
0answers
8 views

Is there any correlation between approximation trendline parameters?

Let's say I have two data sets $(x,y)$ and $(p,q)$ and two approximation trendlines: Logarithmic: $y = b·ln(x) + a$ Linear: $y = bx + a$ Let's say I applied logarithmic approximation to both data ...
0
votes
1answer
40 views

Variant of linear regression using perpendicular distance instead of vertical

Normally, linear regression asks for a pair of parameters m,b such that for a set of given points $\{x_i,y_i\}$ the variance of $y-m\cdot x-b$ is minimized (this minimizes the distance in y-direction ...
0
votes
0answers
19 views

Compute mean of posterior distribution given prior

Is there a formula to compute the mean/expectation of a posterior distribution given the prior? In the ridge regression context, for example. I have $Y=X\theta + \epsilon$ where $\epsilon$ ~ $N(0, ...
0
votes
0answers
9 views

Derivation of log maximum likelihood for multiple target variables

So I'm working through Pattern Recognition and Machine Learning from Bishop. In chapter 3.1.5 he generalizes fitting a function to multiple target variables. Ultimately, we have the function: ...
0
votes
2answers
45 views

How to calculate parameters of a logarithmic approximation trendline?

I have a set of (Y) data $\left\{y_1, y_2, ..., y_n \right\}$ and a set of (X) $\left\{x_1, x_2, ..., x_n \right\}$ which I use to build a graph. I need to place a logarithmic trendline over the ...
0
votes
0answers
24 views

Weighted average of slope

I'm trying to find the weighted average of a temperature increase in a vessel. So, essentially the weighted average of a temperature over time. I'd like some input if this equation gets me what I'm ...
0
votes
0answers
15 views

P value graph meaning

What is the meaning of this graph? Why there is a p-value/2 in the right and not in the left?
0
votes
0answers
14 views

Given a confidence interval for B1, determine a confidence interval for the change in mean of Y

I have a simple linear regression model: $Y = B_{0} + B_{1} * X + e$ I determined a 95% confidence interval for $B_{1}$: $[-1.873 * 10^{-5} , -1.095 * 10^{-5}]$ And then the second part of the ...
0
votes
2answers
52 views

How to apply the method least squares polynomial of single degree?

Now I am making Almon model. Lag is 3, and polynomial of 2 degree, so I have following linear regression equation $y_{t}$ = $a$ + $c_{0}$$z_{0}$+ $c_{1}$$z_{1}$+$c_{2}$$z_{2}$. I have a list of ...
0
votes
0answers
18 views

Do Monte Carlo perturbations capture all the uncertainty in prediction?

I have a model $M$ that I use to predict a value $y = M(\vec x)$. I have known one-$\sigma$ error bars on each input $x_i \in \vec x$. I want to know the one-$\sigma$ error bar on my prediction $y$. ...
0
votes
0answers
15 views

multiple regression Brown-Forsythe

I have a multiple regression model with three variables: $Y$= Labor Hours $X_1$= Cases Shipped $X_2$= Costs $X_3$= dummy variable which gives a $1$ if it falls on a holiday and $0$ if it does not. ...
0
votes
1answer
28 views

Least Square Estimators of a Linear Regression Model

A linear regression model may be written either: $Y_i$ = $\beta_0$ + $\beta_1X_i$ + $\epsilon_i$ Or $Y_i$ = $\alpha_0$ + $\alpha_1(X_i + \bar x)$ + $\epsilon_i$ Use the method of least square to ...