The parameters of a regression model.

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analytic problem on the R^2 and LSE [on hold]

I'm stuck in #7 and #9 for hours. how can I solve these problems?
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12 views

Linear spline coefficient

I am looking for help in interpreting the coefficients of linear splines. I have read everywhere that a linear spline coefficient is the degree of the change in the outcome with every unit increase in ...
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1answer
47 views

Simple linear regression and sampling

I have a small dataset (60 elements) for which I fit a simple linear regression model, and obtain a small coefficient of determination ($R^2 = 3\%$). I'm a beginner in statistics so I'm trying to ...
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23 views

creating a equation for non linear multiple regression to predict a value based on the inputs given in excel

I have data with 5 columns namely Botany,Zoology,Chemistry,Physics and Rank in a excel sheet . The data here is non linear . So I want to generate a equation in the form of y=a+bx1+cx2+dx3 In ...
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1answer
51 views

Interpreting intercept for the log model in linear regression in R for small predictor

I have a dataset. Assume that y is the dependent variable and x is the independent variable. My goals for this analysis is mainly on the following hypothesis: Expecting x=0 to imply y=0 Expecting ...
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31 views

How to proof relationship between inverse covariance matrix and linear regression coefficients?

Edited: I would like to work out the above relationship, more precisely: Let $(Y_{1}, ..., Y_{m})$ be a zero-mean vector with covariance matrix $\Sigma$, and let $S \subset \{1, ..., m\}.$ The ...
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2answers
30 views

Regression produces a high coefficient of determination, but also a high MSE

I've ran several regression models on a dataset (the SEER cancer dataset). I'm trying to use regression to calculate how many months a cancer patient can expect to live. Each record consists of around ...
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2answers
25 views

efficiency - bias trade-off

Under which conditions would a researcher choose optimally when there is a trade-off between the variance and bias of an estimator? I hope this question is not too broad... Any help would be ...
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11 views

Describing the association between dependent and independent variables [duplicate]

I’m somewhat confused about the (wording of the) interpretation the coefficient (b1) of a classic OLS regression: Y = b0 + b1*X + e In the literature, the two interpretations: b1 reflects the ...
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1answer
132 views

Does fixing coefficients in a regression make sense, and if so how to do it?

I have a generic question about whether it might sometimes make sense to fix specific regression coefficients to predetermined values. And if this makes sense in particular cases, how do you best go ...
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2answers
25 views

Positive coefficient but negative marginal effect in mlogit

Is it plausible to have a positive coefficient with a negative marginal / impact effect after running multinomial logit model?
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1answer
55 views

Imputation model: Pooled model is insignificant. How to interpret?

I have ordinal data on three IVs ranging from 1 to 5 as below: IV1: Not at all Important - Very Important IV2: Not at all Satisfied - Very Satisfied IV3: Performs much Worse - Performs much better ...
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31 views

Confidence interval for a regression parameter via prediction

Consider a simple Poisson-regression - GLM - model. There $\exp\left(\beta\right)$s are used as Incidence Rate Ratios (IRR), but their calculation is sometimes not completely straightforward, for ...
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52 views

Population parameters of a regression

So this has really been bothering me and I was hoping for a (simple!) explanation if possible. Suppose I've specified a linear regression model: $$ Y = \beta_0 + \beta_1 X + \epsilon $$ And an ...
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1answer
33 views

Issues in estimation and plot

I am learning adaptive filters and testing the performance of using Least Squares and Kalman filter for parameter estimation for $y = X + \text{noise}$. The model is autoregressive AR(2) model $$y(t) ...
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35 views

How to interpret Dickey Fuller (DF) test results in R (for unit test)

I read 1) Intuitive explanation of unit root and 2) http://www.r-bloggers.com/unit-root-tests/ for doing unit root test. I have basic questions: 1)should I check for unit root on both 'x' and 'y' ...
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Regression equation formatting

I have a simple question for you, which has to do with style. Since I am a novice in writing research papers, I have the small issue of not knowing how to represent an equation in an acceptable way. ...
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2answers
40 views

Test for equality of coefficients from 2 different samples

I have a model that I fit on two different samples (each representing a region in a country, with different sample sizes): ...
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12 views

Change in regression coeficient using multiple regression [duplicate]

I have a simple question: I'm using mutiple regression to assess various background information as predictors of mental health. When adding more predictors, the dummy coded variable of being born in ...
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2answers
79 views

Testing slopes in multivariate adaptive regression splines (MARS/earth)

I am using the earth package in R to estimate the number of breakpoints in a curve. There is only a single predictor. I was ...
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2answers
31 views

Model regression of means different size and variance

I want to explain the relation between getting a reply and posting in a e-commerce. I want to know how much a reply increases postings. I know I could do a regression of postings=f(replies) but the ...
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1answer
66 views

Multivariate model and large regression

I am not familiar with the concept of multivariate model and just learning about regression model. I am familiar with Autoregressive model and Moving Average. Multivariate regression model provided ...
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10 views

Signal dimension in regression model

Estimating Unknown Sparsity in Compressed Sensing is a paper about sparse signal. I am just learning the concepts. In the first paragraph, it says that when the number of observation data samples $n$ ...
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15 views

Comparing beta estimates within the same sample, same independent but different dependent variables

I have a GLM with 5 independent variables (Gen-Score (GS) (independent variable of interest), Gender, Age, Sibship and year of birth) and I want to show that the GS predicts measurements of lean mass ...
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28 views

Estimate linear regression using items randomly selected from an item pool

I am asking this question against the background of a linear regression with single predicted variable $Y$ and multiple predictors $X$. $X$ comes from a survey using an "item pool" which suggests that ...
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34 views

Interpretation of the coefficient of dummy regression?

I found this for a week, but I still cannot find anything about it. In a regression, Y = a + b * X + controls +e If we add dummy D=1 for group A and 0 for others, it becomes Y = a + b*X + c*D + ...
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60 views

Why is the ratio of $B$ and $e^{B}$ for some variables very large?

I want to know how variables affect travel mode for different trip purposes (i.e. leisure trips, work trips and shopping trips) in a specified region. I have 450 respondents in three different ...
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1answer
30 views

Understanding Regression vs. Means/Median Results

I am having a little difficulty understanding my results - could someone help me understand how to interpret, and if my process is sensible? Here is an example of what I am doing I am trying to ...
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1answer
15 views

Interpretation of two indexes Interaction Term

Respected Fellows. I will thankful if someone help me to explain my model results.my model is as follows. Yit=αPFit+βPSit+δ (PF*PS) it+εit Where Y is GDP per capita PF=Political Freedom Index ranges ...
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1answer
69 views

How to capture & present lm model output from R

After running iterations of lm() in R, I am now stuck with which components of the model's output to present and how to present them. I know that the $R^{2}$ value, ...
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1answer
132 views

Compare coefficients from two separate panel regressions in Stata

I am trying to compare the coefficients of two panel data regressions with the same dependent variable. What I am aiming at is the following: ...
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19 views

What is a “concordance score” for regression coefficients?

I came across this "concordance score" in a set of slides called Penalized regression methods for ranking variables by effect size, with applications to genetic mapping studies, by Ji Zhu: $$ ...
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1answer
81 views

Calculate coefficients in a ordinal logistic regression with R

Following the question about manually fitting logistic regression, can someone provide the same 'manual' way to fit a ordinal logistic regression with ordered categorical response?
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15 views

Multidimensional Scaling - external scale regression using standardized or unstandardized weights

I am having trouble determining whether to use standardized or raw regression weights when using multiple regression to interpret Multidimensional Scaling plots. Different textbooks seem to advocate ...
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3answers
153 views

How to interpret coefficients of $x$ and $x^2$ in same regression

If I have the below functional form for an OLS regression, how do I interpret the $x$ and $x^2$? I cannot interpret them separately, correct? Do I interpret them as a summation of the two ...
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1answer
72 views

Orthogonalizing predictors for least squares estimation

I know that orthogonalization in LS is to avoid inverting X'X. The idea behind it is to find variables Z that are orthogonal to each other. Although the process to find those is clear to me, I don't ...
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39 views

Aggregating pooled regression outputs in different years

I performed multiple pooled cross-sectional regressions with the same time-intervals (5years) in different years. I'm wondering now on how to aggregate the different regression outputs. Does it make ...
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41 views

Compare regression coefficients within one sample

I run two univariate linear regressions within one sample (same subjects, two different conditions). Now I would like to know how to compare the regression coefficients in order to find out whether ...
5
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1answer
118 views

Is there a way to use the covariance matrix to find coefficients for multiple regression?

For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, ...
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1answer
28 views

Standardizing single coefficient in multivariate analysis

I have panel data and for the I have a following equation $$ logY = \beta_1 + \beta_2 logX + \beta_3 m logW $$ Problem is with $\beta_3$ coefficient. Since m is outside the log and it is a very ...
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1answer
95 views

Linear regression without intercept - sampling variance of coefficient

I am comparing linear regression with and without intercept for the general sampling case. For this, I have $n$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y ...
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2answers
160 views

Do coefficients of logistic regression have a meaning?

I have a binary classification problem from several features. Do the coefficients of a (regularized) logistic regression have an interpretable meaning? I thought they could indicate the size of ...
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1answer
40 views

Why can certain variables in a multiple regression not be included in logarithmic form?

I have a multiple regression equation where log(salary) = b0 + b1(ceotenure). What is the purpose of putting the dependent variable in logarithmic form? How would you interpret the change in y for a ...
2
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1answer
39 views

Coefficient of Determination: For the perimeter and area of a square: Why different?

When calculating the coefficient of determination for a square, why is it that if you use the data set for the side length of as X= (1,2,3,4) and the perimeter as Y=(4,8,12,16) the Coefficient of ...
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3answers
177 views

Is it possible in R (or in general) to force regression coefficients to be a certain sign?

I'm working with some real world data and the regression models are yielding some counterintuitive results. Normally I trust the statistics but in reality some of these things can not be true. The ...
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1answer
52 views

Is the statistical significance of a regression meaningful if it has poor out of sample performance?

I want to determine the significance of a particular variable, among many confounders. If I fit a model on the training set and observe a small p value, should I discard the model because it ...
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1answer
135 views

Regression coefficients with longitudinal data yields different results in R and SAS

I have a question about SAS and R. For a research, I used a longitudinal data and I initially used SAS (GLIMMIX) and then I analyzed the data with R (...
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37 views

How to interpret log-log regression coefficients for other than 1 or 10 percent change?

I have read many threads here on how to interpret coefficients in a regression where the predictor and the dependent variable are log-transformed. Most give an answer for a one or ten percent change. ...
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75 views

Coefficients from a Dynamic Panel Data Model of Economic Growth

I am having difficulties with the interpretation of the regression results from estimating a growth regression in a dynamic panel data set-up, estimated using Stata. (I'm using difference GMM and ...
3
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1answer
101 views

Sampling distribution of regression coefficients for normally distributed random variables

Based on $N$ realizations of two random variables $X \sim N(0,\sigma_X^2)$ and $Y \sim N(0, \sigma_Y^2)$ with correlation $\rho$, I conduct a simple linear regression $Y = \beta_0 + X\beta_1 + ...