Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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Maximum Likelihood Formulation for Linear Regression

I have seen the following for maximum likelihood estimation (MLE) for linear regression in multiple sources, e.g. here: $\mathcal{D} \equiv \{(x_1, y_1), ..., (x_n, y_n)\}$ I do not understand how ...
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6 views

Proving regression satisfies SLR 4 (zero conditional mean assumption)

I have a linear regression as follows and it is assumed SLR1-SLR3 are satisfied: $ sav = \beta_0 $ + $ \beta_1 inc$ + $u$, where $ u = inc^{2} \times e$ And $e$ is a random variable with the ...
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8 views

What is the proof that the multivariate standardized Beta coefficients can be derived from the correlation matrix?

According to the source below, $B_i=R_{ii}^{-1}R_{iy}$ where $R_{iy}$ is the DV & IV correl vector and $R_{ii} $is the IV correlation matrix. To convert to the unstandardized Betas, multiply by ...
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4 views

Creating a meaningful metric from a multiple regression residual

I want to show a scatter plot and accompanying best fit line for a regression equation I am using for, say, number of cigarettes smoked (x-axis) predicting visible skin blotches (y-axis). A ...
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7 views

Comparing Parameters Estimates between two linear models

My question is regarding comparison of parameters estimates of two different models. The first model is Y~ constant + b1 * X1 + error and my second model is Y~ constant + b1 * X1 + b2 * ...
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43 views

Find Variance of AR(2) process $X_i = 0.3X_{i-2} + u_i$

Full question: $X_0,X_1, …., X_n$ are distributed according to the following AR(2) process $$X_i = 0.3X_{i-2} + u_i$$ for $i=1,...,n$, $X_0=X_1=0$, and $u_i$ are iid $N(0,3^2)$. Have no idea ...
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11 views

Notational issues for point estimates

In the most basic form, (as I recall), consider a random variable $X$ which is defined over a probability space $\Omega$. Now, let us call a realization of $X$ as $x$ . As such, we can define ...
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12 views

Including both individual and state fixed effects

Consider we have the following regression model: $$y_{it}=x_{it}'\beta+\alpha_{i}+\upsilon_{it}$$ where we have data on $N$ individuals for $T$ time periods. Now, if we estimate $\beta$ by ...
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4 views

Hedonic regression - demand measured by number of bookings as DV?

I have the following issue. I am using a dataset with web-scraped data from a sharing economy platform, i.e. the content of the listings as can be seen online. The data thus includes among others the ...
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11 views

Can (how) you enter control variables in a binary logistic regression?

I'm running a binary logistic regression to test whether personality ratings (scale of 1-5) predict a binary outcome, in children. I want to enter factors such as age and gender as control variables, ...
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19 views

Significant in bivariate regression, but not significant in multivariate regression

I have two variables A and B, predicting X. The variables were entered in a two stage hierarchical multiple regression, with variable A entered in Stage 1, and Variable B entered in Stage 2. The ...
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9 views

Loss function selection for weighting errors differently

I am building a regression model where I want to score/optimize/train 'over-predictions' to be twice costly as under predictions. I am attempting to do this in R and hopefully with caret package. ...
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2answers
72 views

Gradient descent: compute partial derivative of arbitrary cost function by hand or through software?

I'm a software engineer, and I'm working my way through Stanford professor Andrew Ng's online course on machine learning. I'm able to follow most of the math related to gradient descent for linear ...
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46 views

Why coefficient changes sign between linear and logistic regression?

My dependent variable $Y$ is continuous a linear model is estimated: \begin{equation} Y = \beta_{0} + \beta_{1} X + \epsilon . \end{equation} I transform the dependent variable into $Z = 1 \text{ if ...
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1answer
16 views

Accuracy in neural network for regression

I want to measure the accuracy in neural network that performs regression. I have two outputs. Is the root-mean-square deviation ( RMS wiki) the right way to go? From wikipedia RMSD is a good ...
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29 views

Different coefficient values from multiple versus bivariate regression

I wonder how to generate such data, so that in single variable regression feature coefficient would be positive, and in multiple regression would be negative. So I read several related questions on ...
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23 views

Model selection: OLS vs TLS

I have two sets of real-valued data and I am interested in their correlation. From my perspective, there appear to be errors both variables, so I am inclined to perform a regression with TLS (Total ...
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27 views

What cross validation use with time series database?

I'm using a regression tree to predict/forecast a daily bases data. I'm wondering to use a cross validation to train and predict all the data. What cross validation procedure I may use?
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8 views

Design constraints for modelling random effects

Consider an experimental design for a target finding study in a computer environment with three factors: display size (small, medium, large) noise (small, medium, large) presentation method (A, B, ...
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13 views

standard error for cofficient in simple linear regression [on hold]

it looks like there is a difference between 5.085 and 5.091, is it just a round-off error?
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1answer
25 views

Interpretaion of Logistic Coefficients

All, I ran a logistic Regression on a set of variables both categorical and continuous with a binary event as dependent variable. Now post modelling, I observe a set of categorical variables showing ...
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2answers
28 views

Time fixed effects - inclusion of time-invariant variables possible?

I am running a regression with panel data and there are some variables that do not change over time (industry,...). As I do not want the time trend to influence my results, I decided to use a time ...
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1answer
9 views

What kind of assumptions do I need to test when running a fixed effects panel model?

I am running a regression analysis on a panel data set. The Hausman test and the logical setup of the research question indicate that a fixed effects model would be best for running the regression. ...
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6 views

Why are the marketing-mix variables measured as period to period percent changes in the generalized bass model?

In the paper Why the Bass Model Fits without Decision Variables, Bass et al. extend the Bass model of product diffusion to incorporate marketing mix variables. For example, if the forecaster ...
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25 views

Assessing calibration plot

I am curious about calibrating a probability estimate, namely a logistic regression. With the example below the outputted calibration plot shows bad calibration with the estimate, or the non ...
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16 views

Test for difference between linear regression lines

I'm trying to find if there is a statistically significant difference between two linear regression lines that I've generated based on two sets of data, does anyone know what test I can used to assess ...
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33 views

Alternative to beta regression

In the data that I am working on, my response is a proportion ranging between 0 and 1. I learnt that beta regression is probably the best choice to model such data, but is there a suitable alternative ...
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24 views

linear regression matlab

I have three predictor variables A: binary (A = vector of length N containing 0 and 1) B: three categories 1, 2, 3 (B = vector of length N containing 1,2 or 3) C: continuous (C = vector of length ...
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37 views

What is meant by using a probability distribution to model the outputs for a regression problem?

Often a theoretical text will say something like, 'a probability distribution may be used to model the outputs' or, 'assume a probability distribution such as normal or Lognormal for the outputs'. ...
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12 views

Dynamic regression models in SAS

Could anyone please advise on any relevant material on utilising dynamic regression models in SAS? The response variable is a continuous variable with multiple drivers with various types (categorical, ...
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41 views

How to studentize residuals

The lecture slide (from PennState Eberly College of Science, STAT 501, Lesson 11.3) says "an ordinary residual divided by an estimate of its standard deviation", but the standard deviation for ...
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8 views

Predicted values poisson family using cv.glmnet

I am a little bit confuse with the values predicted when using cv.glmnet with poisson family. I am using this model because my response variable is counts, but when a use the function predict with s ...
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21 views

Time Series Regression With Splines

I have time series data for 63 years on 3 variables (V1, V2 and V3). I need to fit the most appropriate time model to all three variables individually (linear trend, quadratic trend, cubic trend and ...
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34 views

Why Use Two Different Tests for Existence of Linear Regression: Value of $R^2$ vs $H_0$: slope $= 0$

I am trying to understand better the tests used to determine the existence of a linear relation between two variables $X$,$Y$. AFAIK, one way of testing the strength of any linear relationship is by ...
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37 views

A model for repeated treatments and repeated outcomes

I have the following data: Measurements of kidney function (in units called GFR) taken at several time points pre-operation (not evenly spaced) and at several time points post-operation. Here's my ...
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3answers
65 views

Why does the sum of residuals equal 0 from a graphical perspective?

I've seen the proof for why in least squares regression the sum of residuals is always equal to 0, and I kind of understand why from that algebraic perspective. Basically, you're finding the minimum ...
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28 views

Calculating income elasticity of demand

My model is as follows: $$Y=\beta_0+\beta_1X_1+\beta_2X_2+\beta_3X_3+\beta_4X_4.$$ My income variable is represented by $X_2$. When it comes to calculating the income elasticity of demand (demand ...
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57 views

Can I leave out certain variables that might be accounted for?

I have a dataset that I am trying to use to predict a patient's outcome based on a bunch of factors related to the pateint's care. One of the independent variables is a unique ID number of the ...
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17 views

Error in Pearson correlation, 'y' must be numeric [on hold]

I'm running a regression modelling with GLM between train and validation variables. All the variables are in numeric values. But there is an error when i try to run correlation with an error: 'y' must ...
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24 views

What do my residuals say about my data?

I am new to R and I am trying to find a relationship between Wing length (mm) and Weight (g) of black-capped chickadees using a data set of over 4000 data points. I did a regression analysis and ...
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14 views

Is regression line (for a simple “Y given X” regression, no interaction etc) always unique?

Is it possible for more than one "linear regression" line to fit a given set of points? (i.e.... "least squares" is minimised equally in both cases) I'm assuming a simple one-variable regression in ...
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31 views

Using F-test for (generalised) linear models

I am working with regression on a data set and I am looking for a way to compare the results. From the data ($x$) and observed values ($y$) where $y\in[0, 1]$, I have three models: 1 (baseline): ...
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11 views

sample size for time dependent binomial distribution or logistical regression?

Background I have a membrane of roughly 30000 individual cells that is being flexed back and forth. After some time it fatigues and individual cells start to break. for example after 2000 times being ...
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Comparing Performance and Determining Scaling

My understanding of statistics is fairly basic, but I'll try to be precise here. Method X of doing something exists and can be timed with a particular method of ...
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6 views

A linear model for testing difference in pairs value between two groups

I have the following experimental design: Values of expression of 3 genes taken from 3 different patients and 3 different controls. R code for generating these data: ...
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13 views

Use of data not captured in a survey for survey glm model

A former statistician in my organization carried out a survey to understand customer satisfaction using stratified sampling. On arriving at the organization, I was interested in seeing how variables ...
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23 views

Difference between pairwise t test and multivariate linear regression results

I got different results when comparing means of different groups using a pairwise t test and multivariate linear regression. ...
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11 views

Scale a coefficient in a regression

Can I multiple a coefficient by 100? For example, Y= b0 + b1Distance Distance is in metres If I increase distance by 1 metre, Y increases by b1. Multiple b1 by 100, my interpretation is: If I ...
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27 views

Multiple binary logit regressions vs multinomial logit regressions? [duplicate]

Lets assume we have a dependent varible which can take on three values: 1, 2 and 3. Is there any differences in running multiple binary logit regressions(ie. 1 vs 2 and 2 vs 3) or the multinomial ...
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58 views

Is my understanding of regularized logistic regression correct?

I learned that regularized logistic regression helps prevent the model from over-fitting the data. I understand that the function is still technically a high-order polynomial, but the effect is ...