Questions tagged [regression]

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

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6
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1answer
2k views

Non-parametric regression

I am conducting a mulitple first order regression analysis of genetic data. The vectors of y-values do not all follow a normal distribution, therefore I need to implement a non-parametric regression ...
12
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3answers
47k views

Can I use multiple regression when I have mixed categorical and continuous predictors?

It looks like you can use coding for one categorical variable, but I have two categorical and one continuous predictor variable. Can i use multiple regression for this in SPSS and if so how? thanks!
6
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1answer
8k views

Splitting one variable according to bins from another variable

I have continuous data "A", binary categorical data "O", gender/sex and age for several participants in a study. A linear model in R shows no correlation between A and age. I would now like to ...
11
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4answers
723 views

How to present the gain in explained variance thanks to the correlation of Y and X?

I'm searching how to (visually) explain simple linear correlation to first year students. The classical way to visualize would be to give an Y~X scatter plot with a straight regression line. ...
3
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3answers
6k views

What does RMS stand for?

A physics application I'm using reports for a first order fit of the three points below as $11.388612x - 301.878$. x, y 35, 0 430, 4861 656, 7000 It ...
17
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1answer
13k views

Fitting models in R where coefficients are subject to linear restriction(s)?

How should I define a model formula in R, when one (or more) exact linear restrictions binding the coefficients is available. As an example, say that you know that b1 = 2*b0 in a simple linear ...
15
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5answers
11k views

How to model prices?

I asked this question on the matemathics stackexchange site and was recommended to ask here. I'm working on a hobby project and would need some help with the following problem. A bit of context Let'...
6
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2answers
21k views

Can the multiple linear correlation coefficient be negative?

I am using IDL regression function to compute the multiple linear correlation coefficient... ...
5
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1answer
2k views

What is the prediction error while using deming regression (weighted total least squares)

Deming Regression is a regression technique taking into account uncertainty in both the explanatory and dependent variable. Although I have found some interesting references on the calculation of ...
3
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1answer
2k views

Why are my constraints getting dropped?

I'm currently applying the Roy Zelner test of poolability as shown in the excellent article of Andrea Vaona, in fact I'm working with panel N=17 T=5, and my model looks like this : $$Y_{it}= a_0+...
5
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2answers
5k views

R-squared result in linear regression and “unexplained variance”

I did a linear regression in R and got the following result: ...
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1answer
2k views

Interpretation of log likelihood and covariate significance in Cox regression

Another newbie question here (probably piece of cake for you guys). When I run a Cox Regression and one of my covariates come out as significant: ...
1
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1answer
732 views

How to handle age at measure-start in Cox regression?

I'm a statistics newbie (medical student) trying my luck with a Cox regression for a survival analysis on the outcome of a specific type of operation. And I'm trying to determine which variables to ...
98
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3answers
94k views

Does an unbalanced sample matter when doing logistic regression?

Okay, so I think I have a decent enough sample, taking into account the 20:1 rule of thumb: a fairly large sample (N=374) for a total of 7 candidate predictor variables. My problem is the following: ...
4
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2answers
6k views

Evaluating effect sizes of interactions in multiple regression

I have been running 3-level multilevel models with HLM, and my main interest is in some cross-level interaction effects that I am finding. My concern is that the effect sizes of these interactions ...
18
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2answers
79k views

How do I interpret Exp(B) in Cox regression?

I'm a medical student trying to understand statistics(!) - so please be gentle! ;) I'm writing an essay containing a fair amount of statistical analysis including survival analysis (Kaplan-Meier, Log-...
5
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2answers
186 views

Effectively fitting this kind of model: $y = c_1 (x_3 - x_4) + c_2 (x_1 - x_9)$

Given observations of $\{y, x_1, x_2, \cdots, x_n\}$, we can always do a linear regression and get all the coefficients $\{c_i\}$ for the model $$y = c_0 + c_1 x_1 + \cdots + c_n x_n.$$ However, ...
26
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7answers
23k views

Estimating a distribution based on three percentiles

What methods can I use to infer a distribution if I know only three percentiles? For example, I know that in a certain data set, the fifth percentile is 8,135, the 50th percentile is 11,259, and the ...
3
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3answers
1k views

Regression with an unknown dependent variable - estimating “likelihood” to do something

This probably seems like a really strange question, but let me try to explain what I want to do; hopefully it will make sense. I have a data set with a couple dozen variables, such as age, level of ...
5
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3answers
2k views

Can you use heteroskedastic time series variables within a regression model?

We are working on a multivariate linear regression model. Our objective is to forecast the quarterly % growth in mortgage loans outstanding. The independent variables are: 1) Dow Jones level. 2) % ...
46
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5answers
1k views

Understanding regressions - the role of the model

How can a regression model be any use if you don't know the function you are trying to get the parameters for? I saw a piece of research that said that mothers who breast fed their children were less ...
10
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1answer
6k views

Plotting a piecewise regression line

Is there a way of plotting the regression line of a piecewise model like this, other than using lines to plot each segment separately, or using ...
12
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3answers
5k views

Understanding SVM regression: objective function and “flatness”

SVMs for classification make intuitive sense to me: I understand how minimizing $||\theta||^2$ yields the maximum margin. However, I don't understand that objective in the context of regression. ...
15
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4answers
6k views

Confidence intervals for regression parameters: Bayesian vs. classical

Given two arrays x and y, both of length n, I fit a model y = a + b*x and want to calculate a 95% confidence interval for the slope. This is (b - delta, b + delta) where b is found in the usual way ...
10
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2answers
11k views

Knot selection for cubic regression splines [duplicate]

I was wondering if anybody had experience in how to set the knot points when using cubic regression splines. Some background: I have a response and predictor variable, and I want to determine the ...
6
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1answer
2k views

Leave-one-out cross validation and boosted regression trees

Colleagues of mine recently presented a work where they calibrate boosted regression trees (BRT) models on small data sets ($n= 30$). They validated the models using leave-one-out cross validation (...
6
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1answer
4k views

How to tell if the slope of a line is 0 or there is just no relationship?

I am attempting to examine the change in slope between a predictor and response over two years. In year 1, it is definitely positive. (Linear regression, the 95% CI of the slope doesn't overlap 0). ...
3
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1answer
163 views

When is it better to average observations at the same abscissa?

If you want to regress y on x, where multiple y's are observed at each x, is it ever better to instead take the mean at each x, and the use those means for the regression? Does it depend on the ...
9
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4answers
12k views

Partialling or regressing out a categorical variable?

Occasionally I see in literature that a categorical variable such as sex is “partialled” or “regressed” out in (fixed-effects or mixed-effects) regression analysis. I'm troubled with the following ...
10
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6answers
10k views

Finding the change point in data from a piecewise linear function

Greetings, I'm performing research that will help determine the size of observed space and the time elapsed since the big bang. Hopefully you can help! I have data conforming to a piecewise linear ...
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3answers
939 views

Confidence interval of slope in linear regression

When computing a confidence interval of slope in linear regression, should you use the z- or t-statistic?
3
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2answers
2k views

Average effect of coefficients across multiple linear models?

I have several OLS models with robust s.e.'s that predict an outcome variable Y. For instance: Model 1: $Y=B_0 +B_1X_1$ Model 2: $Y=B_0 + B_1X_1 + B_2X_2$ Model 3: $Y=B_0 +B_1X_1 + B_2X_2 +...
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3answers
5k views

Comparing regression models on count data

I recently fit 4 multiple regression models for the same predictor/response data. Two of the models I fit with Poisson regression. ...
5
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6answers
19k views

Get the number of parameters of a linear model

Is there a way to get the number of parameters of a linear model like that? model <- lm(Y~X1+X2) I would like to get the number 3 somehow (intercept + X1 + X2)...
26
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4answers
28k views

What if interaction wipes out my direct effects in regression?

In a regression, the interaction term wipes out both related direct effects. Do I drop the interaction or report the outcome? The interaction was not part of the original hypothesis.
5
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3answers
9k views

No valid coefficients for NegBin regression

I am doing multiple regression with some data (5 predictors, 1 response). Since the response is discrete and non-negative, I thought I would try Poisson regression. However, the data are significantly ...
10
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2answers
4k views

How to compute the confidence intervals on regression coefficients in PLS?

The underlying model of PLS is that a given $n \times m$ matrix $X$ and $n$ vector $y$ are related by $$X = T P' + E,$$ $$y = T q' + f,$$ where $T$ is a latent $n \times k$ matrix, and $E, ...
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3answers
1k views

Which test to find out best concentration (the one having maximum effect)?

Hi my apologies first, I'm a biologist and not so good in statistics. In my study I'm studying the effect of concentration of feed on growth of a certain specimen. I have with me the different ...
10
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4answers
24k views

What are the assumptions for applying a Tobit regression model?

My (very basic) knowledge of the Tobit regression model isn't from a class, like I would prefer. Instead, I have picked up pieces of information here and there through several Internet searches. My ...
42
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3answers
27k views

Why is there a difference between manually calculating a logistic regression 95% confidence interval, and using the confint() function in R?

Dear everyone - I've noticed something strange that I can't explain, can you? In summary: the manual approach to calculating a confidence interval in a logistic regression model, and the R function <...
27
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5answers
78k views

What is the expected correlation between residual and the dependent variable?

In multiple linear regression, I can understand the correlations between residual and predictors are zero, but what is the expected correlation between residual and the criterion variable? Should it ...
2
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1answer
7k views

How to do meta-regression analysis with SPSS?

I have done a meta analysis and heterogeneity is too high. I am working with (even/Total) for experimental and control groups to calculate the Odds Ratio. I have done fixed-effect and random-effect ...
6
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2answers
288 views

Discerning between two different linear regression models in one sample

Suppose I observe a sample $(y_i,x_i)$, $i=1,...,n$. Suppose that I know the following: $y_i=\alpha_0+\alpha_1x_i+\varepsilon_i$, $i \in J\subset\{1,...,n\}$ $y_i=\beta_0+\beta_1x_i+\varepsilon_i$, ...
2
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1answer
215 views

What type of statistical analysis solves this problem?

I have database of 78706 resident incidents in aged care facilities (5 years of data). I want to to learn and implement a tool allowing analyzing these data using following attributes: Resident Date/...
10
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3answers
1k views

Resources for learning about spurious time series regression

"Spurious regression" (in the context of time series) and associated terms like unit root tests are something I've heard a lot about, but never understood. Why/when, intuitively, does it occur? (I ...
7
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4answers
4k views

Determining trend significance in a time series

I have some time series data and want to test for the existence of and estimate the parameters of a linear trend in a dependent variable w.r.t. time, i.e. time is my independent variable. The time ...
266
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2answers
193k views

Interpretation of R's lm() output

The help pages in R assume I know what those numbers mean, but I don't. I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. ...
2
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2answers
2k views

How can I find the best linear combination of a set of matrices to approximate a target matrix?

I want to find $\theta$ such that $ \theta = argmin_{\theta} \left( \left|\left| Y - \sum_{i=1}^k \theta_i X_i \right|\right| \right) $ where $X_i$ and $Y$ are N x N matrices and $\theta$ is a ...
4
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1answer
208 views

In a linear regression whose components can also be broken down, is it better to do multi-layered regression, or flatten to final components?

Consider a series like CPI (inflation), which I know is composed of a series of component prices (e.g. meat prices, grain prices, non-food prices, etc.), which in turn are also composed of a series of ...
9
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2answers
2k views

How to test if the slopes in the linear model are equal to a fixed value?

Suppose we have a simple linear regression model $Z = aX + bY$ and would like to test the null hypothesis $H_0: a=b=\frac{1}{2}$ against the general alternative. I think one can use the estimate of $...