Questions tagged [regression]

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

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11
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4answers
4k views

What are the differences between stochastic and fixed regressors in linear regression model?

If we have stochastic regressors, we are drawing random pairs $(y_i,\vec{x}_i)$ for a bunch of $i$, the so-called random sample, from a fixed but unknown probabilistic distribution $(y,\vec{x})$. ...
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2answers
22 views

Understanding the causes and implication of heteroskedasticity

I’m trying to heteroskedasticity and how, even if we don’t have MLR 5 assumption (heteroskedasticity), we can still have unbiased estimates. I was thinking: a very intuitive cause of a growing ...
56
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4answers
18k views

What is a contrast matrix?

What exactly is contrast matrix (a term, pertaining to an analysis with categorical predictors) and how exactly is contrast matrix specified? I.e. what are columns, what are rows, what are the ...
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0answers
5 views

Does the model selection in this study make sense?

I was introduced to the following study. It seems to me that they are comparing three groups with a lot of predictors. If this was my study I would have just ran a mixed model or an ANOVA to compare ...
0
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0answers
6 views

In case of “No breakpoint estimated”, should I use only linear regression instead of time segmented analysis in R?

I am trying to do 2-time segmented analysis using the package segmented in R but I am encountering errors that I tried to figure ...
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0answers
8 views

Method of Data-Analysis

For my research I'm examining whether applying a certain promotional intervention improves the amount of misshapen products bought. The study contains of two parts. In part 1 Scanner data from ...
0
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1answer
423 views

Beta coefficient (Partial Least Squares)

Kindly advise if the value of beta is obtained in the results when a Regression analysis, Pearson Correlation or Partial Correlation is conducted. I understand that beta reveals the strength of a ...
1
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0answers
10 views

What are the reasons why a regresion prediction with a threshold cannot be used as classification?

For example, lets assume there are two models: A logistic regression for whether or not it will rain the next day A linear regression for the amount of rainfall tomorrow What are the reason why and ...
0
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0answers
5 views

Valid alternative to Box Tidwell method for Linear Regression [duplicate]

I am building a Logistic Regression model (in sklearn) and want to verify that the assumption regarding the linearity between X and the logit function is correct. I am using Python so am looking for ...
0
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0answers
9 views

Valid alternative to Box Tidwell method for Linear Regression [duplicate]

I am building a Logistic Regression model (in sklearn) and want to verify that the assumption regarding the linearity between X and the logit function is correct. I am using Python so am looking for ...
3
votes
1answer
2k views

Multilevel logistic regression with a random slope(s)

I would like to specify a two-level logistic regression model with random intercept and random slope. Dependent variable: hospitalization (1) or no-hospitalization (0). Independent variables: age, ...
2
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2answers
202 views

Question about sliding differences contrast coding rationale

I've been reading up on sliding differences coding (forward differences coding, on the ucla page: http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm). Here is the contrast matrix recreated ...
0
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0answers
16 views

Calculate probability of outcome of a medical procedure

I have data on medical procedures completed at hospitals in major U.S hospitals. Each medical procedure is assigned a code, for example: Kidney Transplant is X6571. I define the success criteria and ...
1
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0answers
155 views

Reading a pressure gauge with a CNN

Using standard Computer Vision pipelines to read pressure gauges is well established, and not overly accurate or generalizable: For various reasons, I would like to use a CNN to do this. Since the ...
0
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0answers
9 views

Question on Cross Validation Assessment on Training/Validation/Test Sets

I want to make sure I am grasping Cross Validation (k-fold or single validation set) correctly in a high-level sense. The idea is to first split the data into 3 sets, Train/Validation/Test. I train ...
0
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0answers
5 views

orthogonal projection in an algorithmic procedure for LARS

To my best understanding, the steps for Least Angle Regression are as follows: ...
0
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1answer
15 views

Deriving conditional maximum likelihood

When maximum likelihood is used to fit a parameter of a conditional distribution, I often see the argument go like this. We have our data set of experienced tuples $\mathcal{D} = \{(x_1,y_n), \cdots , ...
0
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0answers
17 views

When are two slope coefficients correlated? [closed]

I want to find a variable that has almost linear slope coefficient with another variable, when both are included in the independent variable. That is, Say Y = b0 + b1X1 + b2X2 + u. Is it possible to ...
2
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1answer
33 views

Estimating mean in the presence of serial correlation

Consider the following generating equation: \begin{equation} X_{d+1} = a X_d + b + {\cal E}_d \end{equation} where $a$ and $b$ are constants with $0 <a < 1$ and $b > 0$. Further let ${\...
2
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0answers
18 views

Regression: What is the difference between assuming the covariates are random or not random? [duplicate]

I often see regression expressed in two ways. The covariates are random: In this scenario, we have $(x_i,y_i) \sim G$ for some distribution $G$ and are i.i.d. for $i = 1, \cdots, n$. We then posit $...
0
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0answers
15 views

Does the General Linear Model apply to distributions that are not parameterized by the mean?

In the general linear model, we experience $(x_i,y_i)$, and assume these tuples are generated by some underlying distribution $(x_i,y_i) \sim p_{data}$. We assume this distribution belongs to the ...
1
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0answers
12 views

Causal modelling: specifying model additively or hierarchically?

Let's assume we would like to examine regional disparities in income. We are NOT interested in country-wide effects. A DAG tells us to adjust for age and education. DAGs do not tell anything about ...
0
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2answers
93 views
+50

Solution for equation of log linear regression

Update: I would like to solve a log-linear equation and interpret the final result. I was noted that my question was not complete/unclear. Fine, now I took a dataset from Kaggle as the example to ...
0
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0answers
3 views

Goodness-of-fit for conditional logistic regression in a 1:1 matched case-control study

Dear Stackexchange community; I would appreciate if someone would guide me on this matter. On data analysis of a 1:1 matched case control study based on age and gender through using conditional ...
1
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0answers
20 views

Addressing non-linearity in a fitted vs residuals plot

I am trying to conduct a data analysis project, which involves a multivariable regression model with 13 predictor variables. Before having transformed/ altered the data at all, I fitted a rough model ...
1
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1answer
19 views

Would serial correlation be problematic if only the regressors are serially correlated in a multiple regression model?

In this regression: $Y_t=\beta_0+\beta_1 X_{1t}+ \beta_2 X_{2t} + ... + \beta_p X_{pt} + \epsilon_t$ If there is serial correlation among e.g. $X_{1t}$, what would be the consequence?
0
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1answer
148 views

Which regression to use on percentage as a response variable for ordinal dependent variable?

I have data where for a specific threshold, I calculate what percentage of values meet a certain criteria. I want to calculate whether there is a statistically significant trend when I increase the ...
0
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1answer
20 views

Question regarding Optimal Designs of experiments

I'm a bit unclear on the concept of optimal design of a data matrix $X$. I propose a small example to work through: Suppose $\epsilon_i \sim N(0, \sigma^2)$ are i.i.d., and I have some experiment ...
0
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1answer
218 views

How linear regression algorithm estimates values and draw line

I am learning Machine Learning. and going through some videos. In that one slide came which I am not able to understand (Attached below). This is related to Linear Regression. In second image, it ...
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0answers
18 views

Gradient descent for regression parameter estimations [closed]

What are the typical step of using gradient descent for regression parameter estimations? (simple linear regression)
1
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1answer
15 views

How to estimate the impact of policy on labor supply if the policy causes death, too?

Suppose people can make only one of three choices A, B, C. A = Death B = Survive, Work C = Survive, Not work I want to study the impact of an exogenous policy on ...
0
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0answers
5 views

allocation (%share or importance) calculation with positive and negative values [closed]

Let say I have three values 20,50,30, if I want to calculate share, this can be calculated as 20/100,50/100,30/100. But let's say the number involve negative values 20,-50,30 how do I calculate share ...
3
votes
1answer
319 views

Graphical proof of variance decomposition for linear regression

Suppose we aim to predict $Y$ from $X$ using the linear regression model $Y = mX + b$. There is a standard variance decomposition: $$\operatorname{Var}[Y] = \operatorname{Var}[\widehat{Y}] + \...
6
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1answer
326 views

minimizer weighted linear regression

In a regression problem, with $y=X\theta+\epsilon$ and $X$ is an $n$ by $p$ matrix the ‘weighted least squares estimate is the minimizer $\theta^{*}$ of $f(\theta)=\sum_{i=1}^{n}\omega_{i}(y_i-x_i^{'}\...
0
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1answer
24 views

Does this graph support an assumption of homoscedasticity?

Does this graphics support the assumption of homoscedasticity?
0
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2answers
33 views

How to model binomial data when the dependent variable is LITERALLY dependent on the independent variable

I am designing an experiment where a subject makes a choice between two options ("low value" (LV) and "high value" (HV)). The subject will experience both options during a trial ...
1
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0answers
14 views

How to prove the equivalence of partial correlation and coefficient of partial determination?

I am taking a regression course. I do not know how to prove these formulae are equivalent. $$ R_{Y1|2}^2 = \frac{SSE(X_2) - SSE(X_1, X_2)}{SSE(X_2)} $$ $$ R_{Y1|2}^2 = \frac{(r_{Y,X_1} - r_{Y,X_2}r_{...
3
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1answer
77 views

Are these two 2D dataset is same, and can be separate with XOR NN?

I'm a very beginner in the neural network topic. So I ran into a problem. I see on the online lectures: Famous example of a simple non-linearly separable data set, the XOR problem (Minsky 1969) in the ...
0
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1answer
13 views

How to predict an event for different time intervals and compute score?

Let's say I have a medical dataset/EHR dataset that is retrospective and longitudinal in nature. Meaning one person has multiple measurements across multiple time points (in the past). This dataset ...
0
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1answer
22 views

How to calculate 28 day mortality?

I have a retrospective EHR database from a hospital and I would like to build an ML model to predict whether a patient will die within 28 days or not (from discharge/some time point T) Can I check ...
0
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0answers
3 views

How to interpret a simple moderation analysis (model 1) in PROCESS Macro on SPSS with 1 continuous IV and 1 categorical moderator?

I'm doing my master thesis on the effect of childhood poverty* (IV) on switching behaviors in adulthood (DV), and I am expecting an increase in the DV only in currently financially stressful ...
1
vote
1answer
212 views

Regression of Stationary Time Series in Non-Stationary Time-Series

Let's suppose that I have a time series $Y_t$ with dimensions $T \times 1$ with monthly frequency, and a matrix of external variables $\boldsymbol{X_t}$ of dimensions $T \times p$ where $p$ also ...
0
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0answers
5 views

How to include random effects in a Chi-square Goodness of Fit test

I'm trying to figure out how to include subject identity (random effect) in an analysis where subjects make a choice between two concurrent options. I found this website, which shows how to code ...
1
vote
1answer
132 views

Comparing two heavily skewed, overdispersed counts

I have, as the title suggests, two heavily skewed, overdispersed histograms. The data ranges from 0 minutes to 85334 minutes. 90% of the data is below 15 minutes, and takes the form of a positive-...
0
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0answers
9 views

Find the Multiple Correlations R12.3 [closed]

A simple correlation coefficient between yield (x1), temperature (x2) and rainfall (x3) are given by r12 = 0.6, r13 = 0.5 and r23 = 0.8. Find the multiple correlations R12.3.
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0answers
27 views

Independent variable is correlated with intercept, creating singularities

I am building a logistic model with about 20 variables. I have used the following code: `fullmod = glm(cancer ~ B_SEX+BLINE_AGE_AT_BASELINE+B_BMI+B_chro+B_fdrc+B_hrt+B_LMET+ B_MET+B_FV+B_EDU+B_INC+...
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0answers
8 views

How to esimate bivariate probit in R [closed]

I want to estimate a bivariate probit such that : Y1~X1+X2+X3 Y2~X1+X2+X3 I want to calculate the predicted marginal probabilities, that is Pr(Y1=1) and Pr(Y2=1). How can I run this model in R and ...
0
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0answers
11 views

detect incalculable variables

I have a bunch of equations in the form as follows. a+b+c+d=10 c+d+e+f=12 d+e+c=13 Where I am tying to calculate the values of each variable (many more equations ...
4
votes
5answers
165 views

confusion about individual notation

Let's say I am trying to estimate the regression of $y$ on $x$: $$y= x \beta + \epsilon.$$ So, when moving to regression frameworks, I often see people use the individual notation: $$y_i = x_i \beta + ...
0
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0answers
16 views

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