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Questions tagged [regression-coefficients]

The parameters of a regression model. Most commonly, the values by which the independent variables will be multiplied to get the predicted value of the dependent variable.

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1answer
113 views

Do demographic variables need to be standardized when population size is included as a covariate?

I am doing a fixed effects regression where the dependent variable is number of people in an treatment facility in a given state/year. We are also including a population size control variable. I am ...
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67 views

Why doesn't using an interaction/effect modification term give the same results as subsetting the data?

I'm interested in the effect of continuous variable A at the two different levels of categorical variable B. I had thought that the following approach would give the same estimates for the effect of A:...
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42 views

Why we choose the least square estimator than another one in regression model?

If we have the linear model $Y_i-\bar{Y} =b(X_i - \bar{X}) + \varepsilon_i,\ i=1,..., n$ , then we can find easily an unbiased estimator $b^*$ for $b$ with the least squares method. If $c=(Y_n - \bar{...
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84 views

Derivation of GLS coefficients in simple regression

Let $y_t = a + bX_t + u_t $, where $t = 1...n, X$ is not random and $x_t \neq x_s$ for $s \neq t$). $E(u_t) = 0, E(u_tu_s) = 0 $ and $ E(u_t^2) = w_t^2$ with $w_t>0$. How do we derive GLS ...
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53 views

Large coefficients in DiD

I am examining whether a regulatory change affects profit margins (PM) and return on assets (ROA) using a difference-in-difference test. Firms are divided into treatment (T=1) and non-treatment (T=0). ...
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81 views

How to Reshape Linear Regression Model using Correlation Coefficient instead of slope?

I try to reproduce Results from Harding and Pagan (2004), p.12, where they try to estimate the correlation coefficient $\rho_{S} = cor(S_{y,i},S_{x,i})$ using regression on $$ \frac{S_{y,t}}{\hat{\...
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50 views

Is there a method for calculating a regression coefficient for an a priori equation (e.g. R^2 for y=x)?

I have a data set where I want to see how well the line y=x describes the variance of y as opposed to a standard regression that tries to examine the best fit, as from a theoretical stand point the ...
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1answer
524 views

Multiple linear regression, standardization and cross validation

I generated 3000 observations (3000) and carrying out multiple linear regression. Prior to regression i randomized my observations five times and then selected 30 % of the observations for testing and ...
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139 views

Restrictions on residuals and coefficients in regression (DFA)

The problem is about Deterministic frontier model, a special case of regression where all the residuals are bound to be positive (non-negative). I have a set of values $PQ$ (x) and quantities $Q$ (y) ...
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753 views

What do r (Pearson correlation coefficient) and R^2 stand for? [duplicate]

As far as I understood, R squared explains how much the variation in Y is explained by its linear association with X. And it's used as an indicator for goodness of fit of a linear model. Then when ...
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637 views

How to improve the accuracy of SVM regression results (has saturation at high values)

I have a question about using SVM regression in matlab. My training data set has a distribution like gaussian (below figure. A lot of data in 0-5, only few data >5). I separate this dataset into 2/3 ...
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783 views

Interpreting Lagged First Differences Linear Regression Coefficents

I am running a Linear Regression Model about housing prices and certain macro variables. My model is as follows: $$House Price_{t+1}=\beta_0 + \beta_1 rent_t+\beta_2 unemployment_t+\beta_1 ...
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33 views

Confidence interval regression issue with quantile data

I am trying to tie out the confidence intervals of the 124.88 intercept on page 8 here: http://www.econ.uiuc.edu/~roger/research/rq/vig.pdf Here is the code: ...
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73 views

Multi-linear Regression Analysis with inter-dependent coefficients

I am forecasting sales based on an e-mail data set. In the the dataset I have sales as well as the quantity of emails sent, the number of unique opens, unique clicks and unsubscribers. I have only ...
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28 views

In the absence of predictor X, target Y is non-zero. what does it mean?

Having this table as a base of analysis that explains linear regression with just one predictor X - TV advertising (in thousands of dollars) and one target variable Y - Sales of a product (in ...
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305 views

Regression line from Anova-table

- I am trying to figure out if it is possible to get the value of $\beta$ for regression line from Anova-table. So far i see that SST = SSE + SSM which is equal to (SST = $\sum(y_i-\bar y))$ ...
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1answer
78 views

Which regression and type of test to use?

I'm trying to find out how stocks and cash react (in terms of returns) when people feel bearish/bullish and when they move asset allocation between stocks/cash. I have three data sets: monthly Dow ...
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1answer
102 views

How does solution of least square analysis change if the output of datapoint is increased by a constant?

What will be the effect on the solution of least square analysis if we apply the following transformations on the training set: add a real number $k$ to the output value of each datapoint. And the ...
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166 views

Normal approximation for Negative Binomial regression

In negative binomial regression, the distribution is specified in terms of its mean, $\frac{pr}{1-p}$, which is then related to explanatory variables as in linear regression or other Generalized ...
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81 views

Relation Between Partial Correlation and Beta Coefficient in Multiple Regression [duplicate]

Suppose I've a multiple regression coefficient in the following form: y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ϵ My question is how to calculate the relationship ...
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1answer
23 views

If multi-level categorical variable misses one coefficient in a model, then has it been omitted or “merged” to the Intercept?

If a model with a multi-level categorical variable is given in the following form: $$logit(\pi_i) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3$$ Where $X_2$ and $X_3$ are the levels $2$ and $...
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33 views

Knowing $R^2$ and sample size

So basically we know $R^2$ and the sample size. How to use these two conditions to find out the largest number of slope coefficient k? Plus in the hint, $K$ is supposed to be very small and we could ...
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1answer
102 views

Illogical probabilities from logistic regression: with example

I have nine variables, age, bmi, duration of disease, fasting blood glucose, diastolic blood pressure, systolic blood pressure, cholesterol, triglyceride, and HbA1c. Using these variables I want to ...
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90 views

Adding an id variable in a linear model causes small coefficient and strange range of fitted values

So I'm trying to construct a linear model on a data set and the data set has an id variable that is a school id. The data set measures (or i.e. the response is) ...
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34 views

How can I ensure the independent features in a dataset have maximum positive coefficients on running logistics regression

I have a sample dataset with about a million records with about 7 feature variables. On running logistic regression on this dataset, I got 5 features with a positive coefficient and 2 with a negative ...
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1answer
280 views

why regress a y variable on a vector of just ones

I am trying to understand some code somebody has written. I have a y vector which is a factor say book to price for 500 companies. Then I also have a x vector of the same shape which is just ones. ...
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462 views

What to do with insignificant regressors in a VECM?

I'm forecasting electricity demand based on GDP and population. For the series that there is a unit root I have conducted the Johansen cointegration test and applied the number of cointegrating ...
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1answer
56 views

Can a variable be statistically insignificant but its components be significant?

There is a paper (here) which shows that the beta coefficient of a standardised variable (see equation 3 in the paper), which represents the correlation between the standardised variables, can be ...
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444 views

Forward selection, using adjusted R square or t statistics?

When it comes to select variable in multiple regression model using forward selection, should we add variables in the models according to its adjusted R square or t statistics/Sig?
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1answer
109 views

Interpretation of Regression coefficient

I have a five-variable regression equation, and I added any constant (fixed value, say 100) to all the observations of variable $A$, another (or same) fixed value in variable $B$, while the other ...
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1answer
150 views

Why doesn't standardization work in the linear regression?

I have a matrix containing the attributes of the item and their corresponding rating. All of the attributes are in the range of (0,1) and the rating is in [1,5]. I transform the range of rating to (0,...
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1k views

How to interpret and explain negative coefficients when they do not make sense

I have seen appearance of negative coefficients where they do not make sense (the data is related to costs where negative coefficient should not appear). If regression models are fitted to individual ...
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340 views

How to interpret nested interactions?

Consider a data set where you have a tenure variable that takes non-negative values (e.g. from 0 to ...
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36 views

Change in coefficients when another factor is included in SEM

I have a question. Let's say in an SEM model, there is a significant relationship between A and B: A-> B (beta=.400). Sometimes if I add another factor (i.e., C) ...
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356 views

Interpreting regression coefficients with a multi-level categorical variable [duplicate]

How do I interpret the coefficients of a Regression w/ 1 continuous + 1 categorical predictor (w/ 4 levels - e.g., months) Specifically, is the 1st coefficient equal to that of the 1st month or equal ...
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1answer
47 views

Binary logistic regression in R - assistance with determining odds of a predictor at different levels

I have performed a binary logistic regression in R with whether or not a sportsperson was re-contracted or not as the DV. My final model is as follows; ...
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198 views

What is the interval of Gini Index?

Suppose we have 2 classes. C1: 0 C2: 6 The Gini index is: $1−(0÷6)^2−(6÷6)^2 = 0$ C1: 3 C2: 3 The Gini Index is: $1−(3÷6)^...
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55 views

Dropping the non-significant parameters in multiple regression

Given the standard multiple linear regression model $$Y=X\beta+\epsilon\sim N(X\beta,\; \sigma^2I)$$ One derives the distribution for the estimated parameters $$\hat{\beta}\sim N(\beta,\; (X^TX)^{-1}\...
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1answer
103 views

Alternative to a coefficient of variation

I am currently collecting data 4x per week with a fencing athlete. She jumps with each foot on a separate force plate, so we can see asymmetries in force curves. We noticed that whenever she is more ...
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1answer
86 views

In count data models with dummies, what exactly means “on average”?

There are some questions + answers out here that explain how to interpret coefficients from count data regressions (e.g. negative binomial), both as incidence rate ratios or marginal effects. Bottom ...
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48 views

The variance of a biased estimator

This builds on an an earlier question from Math SE. I am just starting to learn about the simple regression model. In particular, I am trying to understand what happens to $\hat{\beta_1}$ when the $E(...
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493 views

AIC in R: Back-transformation of model averaged coefficient estimates

I am running an analysis using a mixed model with lmer in R. I am using AIC as my model selection process. I have a global model and am including within the selection process all subset models ...
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1answer
129 views

What is the best way to quantify the goodness of fit between the data and my model?

I am modeling the total fluid rate at the bottom of an oil well using a roughly exponential model (mixed with other terms representing an input signal). Here is one example (blue circles are the ...
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2answers
261 views

DLNM and crossreduce(): getting the coefficients behind the cross-basis

I am using the R package dlnm to fit a distributed lag non-linear model estimated with lm(). One can specify both the exposure ...
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1answer
111 views
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1answer
149 views

Correct interpretation of linear coeffs for 1 interaction, 1 numeric, 1 categorical

Good day, XValidators. This is my 1st question in the community. I'm at my wit's end here. Nowhere in the interwebz nor in youtoubeland can I find an answer to the following: Assume you have this ...
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221 views

Comparing regression coefficients using F-test to assess for batch effects

Here's what I have: two datasets with ~27,000 variables (same variables for each dataset). I'm trying to test whether or not dataset1 and dataset2 display batch effects. Namely, I want to do PCA and ...
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1answer
68 views

Size of Regression Coefficients

I have run a probit regression and the size of my coefficients seem to be quite big with respect to other similar studies. For example, 0.254 vs 1.207 - does this mean anything in particular or is it ...
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57 views

Normalization/Multiple Regression Question

I work in cell culture and normally don't have to use anything more than T-tests, but this project has me stumped... The study design: 1 control treatment and 7 experimental treatments with one ...
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95 views

Using predicted variable among interaction predictors in R

I'm trying to build a model in order to predict a certain variable using the following model: ...