The parameters of a regression model.

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14 views

How do I manually calculate linear multiple regression coefficients? [duplicate]

I am working on an assignment in which I need to manually calculate the coefficients in a multiple linear regression model with 6 predictor variables. I also need to demonstrate my working. I found ...
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1answer
15 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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19 views

Bayesian Variable Selection with NMIG

I have a Bayesian linear model like this: $Y_i = X_i*\beta + \epsilon_i$ . Just for completion: ($\epsilon_i \sim N(0,\sigma^2)$ $\beta \sim N_p(b_0,B_0)$, $\sigma^2 \sim Inv-Gamma (a,b)$) I would ...
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5 views

Interpreting Accelerated Failure Time Coefficients

I feel like this may be a stupid question, so please excuse it if it is--I'm still learning. I have an analysis I'm running using parametric survival analysis, specifically an accelerated failure ...
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1answer
42 views

Interpreting R regression output with multiple interaction variables

Context I am exploring how different factors in targeting affect subjects' self-reported likeliness to purchase a product. Likeliness to purchase was measured on a four point scale: "Very unlikely", "...
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13 views

Selecting polynomial terms in regression

I'm developing a nonlinear response correction for a sensor (to transform "raw.peak" to "target"). I don't care about interpretability. I do care about future accuracy. One might first just throw it ...
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14 views

Choosing polynomial expansion complexity [duplicate]

Here's a specific question I haven't seen asked/answered. Motivation: if you're doing linear regression of two terms plus their interaction, and only the interaction is significant, you keep the ...
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15 views

Hosmer Lemeshow test dependent on cut off value?

when i am building my model in r & looking the goodness of fit test for model fitting, at .5 threshold level, my p value >.05, which tells me that my model is fitting the data well. As soon as i ...
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2answers
59 views

Is logistic regression a valid way of analyzing A/B testing results?

I'm very new to the idea of A/B testing and I want to see if my train of thought here makes sense. Suppose that I run an experiment with two designs. I get two sets of resulting data, one for each ...
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24 views

The significance of existing variables decreases after adding additional variables in regression [duplicate]

I build a simple linear regression, $y=w_0+w_1x_1$. I find the coefficient of $x_1$ is significant. Then I add $x_2$. It shows that the coefficients of both $x_1$ and $x_2$ are NOT significant any ...
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14 views

Interpret log ratio coefficient when outcome is also log ratio coefficient [duplicate]

If I have a log-log regression, where the outcome is change from baseline or: (Δln(Price))=b 0 +b 1 ×(Δln(emp)) Where Δ(ln(emp))=ln(employment growth_year2)−ln(employment growth_year1) and Δ(ln(...
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1answer
16 views

Interpreting lower order effects not contributing to the interaction terms, when the interaction is significant (C in a regression of A + B + C + A*B)

In a regression including 3 variables, and the interaction of 2 of those variables: Variable A Variable B Variable C Variable A * Variable B, where the interaction of Variable A * Variable B ...
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1answer
204 views

Can standardized $\beta$ coefficients in linear regression be used to estimate the $R^2$?

I am trying to interpret the results of an article, where they applied multiple regression to predict various outcomes. However the $\beta$'s (standardized B coefficients defined as $\beta_{x_1} = B_{...
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8 views

Comparing importance of predictors in different datasets in GLM

I want to compare the importance or 'predictive power' of the same feature/covariate in 2 different datasets. Specifically let $[\bf{y}_1,\bf{V}_1]$ be my output & design matrix of dataset 1 & ...
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23 views

Low coefficient of determination and low p-value

What should we think of a regression model that has a low coefficient of determination (e.g. $R^2 = 0.01$) and simultaneously a low p-value ($p<0.01$)? That in reality there is a non-random but ...
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2answers
46 views

How do you interpret a percent variable with a log-transformed outcome?

It doesn't make sense to log transform my x-variable (for a more intuitive elasticity interpretation), since it is already in a % format, but with a log transformed outcome: ln(y) = B0 + B1X1 where ...
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7 views

Optimizing weighting coefficients between series

I am working with a set of predictor variables against a single response factor. This is repeated over several series, all with the same variables. For example, it can be imagined as the predictors ...
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13 views

Negative regression estimates with positive intercept, including dummy and numeric variables

I am running a multiple regression including dummy, count and numeric variables. The dependent count variable is the result of PCA. Multicollinearity tests do not show collinearity. However, most ...
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21 views

unstandardised b coefficient, 95% CI and p-value interpretation in a linear regression

How could I interpret the table when: 1. the unstandardised coefficient has a value equal to 0? 2. either the lower or the upper bound of the 95% CI is 0 but the p-value is less than .05? I just run ...
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2answers
40 views

Transformation of a regression coefficient when independent variable was log-transdormed

In the context of a linear regression model where the independent variable ($X$) was log-transformed, like: $Y = \alpha + \beta·ln(X)$ Is there a straightforward way to transform a regression ...
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10 views

Compare p-value/z-statistic from probit reporting marginal effects with a standard probit without marginal effects

I have results from different empirical studies. Some of them report results for probit/logit models, others report the marginal effects. I want to compare the statistical significance between the ...
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27 views

Comparability of regressions coefficients after aggregation

I have a panel dataset with daily sales information and prices per store. So sales $q_{ij}$, price $p_{ij}$ per day $i$ and store $j$. My primary interest is to estimate the relationship between $q_{...
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28 views

PLS regression in Octave

I'm doing a PLS regression in Octave, using the following function: [XLOADINGS,YLOADINGS,XSCORES,YSCORES,coefficients,fitted] = plsregress(X, Y, NCOMP); From ...
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1answer
54 views

Coefficients linear and log-linear regression model

I performed both a linear and log-linear regression to predict the price of a smartphone based on its characteristics. Now I have a question concerning the coefficients between the two models. In the ...
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13 views

How to calculate regression coefficients in terms of original variables when I already have regression coefficients in terms of PCs? [duplicate]

While doing principal component regression I take the input data, standardize it, calculate PCA, and use the score matrix to solve the equation Y=score*B where Y is my mean-centered known output and B ...
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27 views

Interpreting the regression coefficient when the regressor is polychoric-based principal component

I have a regression where I am trying to interpret the regression coefficient of the first principal component on some outcome variable. The component scores variable was obtained in a polychoric ...
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39 views

How to interpret the coefficients of logistic regression? [duplicate]

I want to understand the interpretation of logistic regression coefficients in terms of an increase in probability of dependent variable being 1. I tested a logistic regression model in R and got ...
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5 views

Summing mixed models regression coefficients

Let's say i have 3 variables. Food, toys and clothes, measuring my big family's expenses. I have tons of observations but my damn kids are horrible bureaucrats, hence i have a lot of missing data. ...
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14 views

Difference between non significant coefficient p-values and variable exclusion using AIC

I am trying to fit a linear regression model with two continuous explanatory variables and one factor with two levels. Rather than predictability, I am especially interested in the interpretability of ...
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12 views

How to report estimate standard errors of levels from a one-way ANOVA

I'm trying to report means of levels given a model. ...
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1answer
70 views

Multicollinearity with highly safe t-statistics but VIF of 13

If all of my coefficients in my logsitic model have really perfect t-statistics that all show sufficiently high significance but have two coefficients that have high VIF like 13-14 with sample size of ...
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1answer
39 views

How to interpret a significant coefficient of 0?

I just ran a multiple regression with 8 predictor variables. Two of them have a significant coefficient, which is 0.000. How can I interpret this? I find it strange that an effect which basically is ...
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Autocorrelation of coefficients for strongly autocorrelated inputs?

In Chapter 5 of "The Elements of Statistical Learning" ("Basis Expansion and Regularization", pg 150"), it is written that Since the input signals have fairly strong positive autocorrelation, ...
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1answer
41 views

Hypothesis testing with quotient of regression coefficients

Suppose we have the following multiple logistic regression model $\beta_0 + \beta_1 X_1 + \beta_2 X_2$, where $X_1$ and $X_2$ are binary variables, and $\theta = \beta_1 / \beta_2$. Then I have two ...
3
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1answer
103 views

Interpretation of coefficients in logistic regression output

I am doing logistic regression in R on a binary dependent variable with only one independent variable. I found the odd ratio as 0.99 for an outcomes. This can be shown in following. Odds ratio is ...
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1answer
10 views

Logit regression and Poisson relative risk estimators

I am running a logistic regression and have determined that Risk Ratios are better to explain my results than odds ratios. I have a dichotomous variable but I have both categorical and continuous ...
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25 views

Sample size of the levels of a categorical variables

Is there a generally acceptable sample size for the levels of a categorical variable included in a regression analysis? For example, if we have a variable color with 3 levels: 5 reds 140 blues 155 ...
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26 views

How do I generate appropriate group-level coefficients and standard errors for my regression?

I ran a mixed logistic model testing the influence of group (two-level) on a binary outcome, and I want to report the group estimates and their SEs in graph. However, I can think of two ways of doing ...
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15 views

Weights vs Correlation Linear Regression

I am working with Spark 1.5 and I want to predict something. Before in R, I would use the p-values from glm and the importance from randomForest to get an idea of feature selection. So, in Spark (...
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1answer
247 views

Regression when response variable is a function

I have a set of data $(X_i,Y_i)$, $i=1,\ldots,n$ where $X$ and $Y$ are supposed to satisfy the following equation $$ y = \beta_0(1+x^2)^{\beta_1},\quad x>0, \quad\quad (1) $$ I am interested in ...
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15 views

To fit a count proces

In R I have data where head(data) gives ...
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1answer
29 views

Measuring Variable Effect in Random Forest Regressor

Is there a way to measure the effect individual predictors have on an outcome for a Random Forest Regressor? If there's not something similar to a regression coefficient, is there a way to utilize ...
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35 views

Interpret coefficients from logit/probit models with inverse definition of dependent or independent variable

I have a couple of empirical studies examining the determinants of credit ratings. Here, the dependent variable is a binary variable indicating whether a firm has a credit rating or not ($rating$). ...
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2answers
45 views

Linear regression on large sparse feature set

I have a sparse feature matrix with 50K observations and 150K features. All features are binary. On this I have to run a linear regression. I want just a decent fit. Data: Let us consider training ...
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1answer
48 views

Manually compute the regression coefficients of a multiple regression model with numerical and categorical variables

I am going to explain my question using a reproducibile toy example. I would like to regress a numerical variable using a multiple regression model with either numerical and categorical variables. I ...
2
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1answer
38 views

How to predict from glm created with average values?

I want to predict count data (example: people visiting a beach) based on some predictors (example: temperature, cloudiness). I have created a generalized linear model (with Poisson distribution and ...
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2answers
77 views

Regression: What is the utility of R squared compared to RMSE?

Suppose I'm doing regression with training, validation, and test sets. I can find RMSE and R squared (R^2, the coefficient of determination) from the output of my software (such as R's lm() function). ...
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1answer
34 views

Heteroskedasticity Question

I have a model that's affected by Heteroskedasticity: bptest(m1) studentized Breusch-Pagan test data: m1 BP = 65.055, ...
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1answer
30 views

Using logistic regression to estimate whether probability of an outcome is greater than chance (and by how much)?

I have an outcome variable that is subjects' correct or incorrect responses to a single question asked at two time points (before and after the experiment). I want to know if subjects were better than ...