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Questions tagged [multiple-regression]

Regression that includes two or more non-constant independent variables.

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OLS Multicolleniarity

I have a pretty simple task to estimate ols multiple regression. I need a measure of multicolleniarity. Is condition number a good measure and what criteria exists fot its value?
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Account for covariate after predictor in ANCOVA?

I've been thinking about ANCOVA a bit and I didn't find anything on this particular issue. One of the most critical assumptions is that the predictor is not correlated with covariate. This is pretty ...
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Liner Regression model bulding - Adjusted R2 [on hold]

While building the Linear regression model step by step, is it mandatory Adjuste-R2 value should keep decreasing from its previous step ? In some scenarios, even if we remove Higher Pr+VIF's variables ...
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Sampling distributions for the slope coefficient

I have a question in my exam, which I do not know exactly the answer, Can you please guide me? Q: Do you believe the sampling distributions for the slope coefficients are at least approximately ...
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1answer
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linear regression backwards elimination

Suppose we have to find the best predictive linear model for the price of residential houses in a certain area from a set of predictors such as sqft, number of baths, etc. Also, suppose that we ...
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Partial regression plot showing vertical line

Partial regression plot showing linearity means variable should be good to use in multiple regression model. Partial regression plot showing curve means variable requires transformation Partial ...
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Incorporating linear combination predictions into multiple regression

Let's say I have a predictor $p_1$ of the form: $\textbf{y} = f(\textbf{x})$ Let's suppose that I found another predictor $p_2$ of the form: $E[y_1 - y_0] = c$ (e.g. I have a predictor of linear ...
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Interpret the slope coefficient

The slope coefficient for SO2 is quite small (0.33), especially as compared to the other three slopes). Does this suggest that the effect of SO2 is therefore not very important?
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1answer
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Meaning of residual maker matrix

Suppose that $M_1$ is the residual maker for a unity vector (i.e. a vector made of $n$ 1's). I am told that this matrix, when premultiplying a variable, transforms the variable "into deviations from ...
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Which command should be used in SPSS for calculating p value without confounding factors effect?

In a study, we have the disease as dependent variable ( 0 or 1 patient or healthy); some independent variables are real and some of them are confounding (some of varibles are quantitative and some of ...
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Is there a formula to convert t-value from a regression parameter to an effect size (d)?

I've seen formulas to convert independent or dependent samples t-tests into effect sizes, but what about converting the t-value from a regression parameter to an effect size?
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1answer
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Interpretation and formulation of SEM path coefficients?

Trying to interpret and write down my SEM results, but not sure if this is 1. correct and 2. well formulated. This is what my models and parameters look like (first unstandardized, then standardized): ...
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Using multiple linear regression instead of survival analysis to estimate time until event

I have just started to read about survival analysis, I have read in this interesting article about survival analysis, and why use it rather than the famous multiple linear regression to estimate the ...
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2answers
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Sensitivity of regression parameters to noise

How sensitive are the parameters obtained from OLS, logistic or other regression methods to noise ? By noise, I mean minor changes. For e.g. adding a small noise $-1<\Delta<1$ to $\beta_1$ in $...
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Which regression model to be used [duplicate]

My dependent variable is classified in categories as 5-10, 10-15 . Which is the best regression model for this kind of analysis.my dependent variable asks the participant of the survey to mark the ...
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1answer
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regression with z-scores as composite variables?

So I have 5 IV's- a,b,c,d,e and one DV. a is fine as is. b & c measure the same concept and since their ranges are the same, I averaged the scores to create a composite variable. d & e ...
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Standard partial regression plot vs. effect plot from 'effects' package

I'll use a modification of this example to ask my question about an apparent alternative way of presenting a partial regression plot, using the effects package. ...
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1answer
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2-step linear regression

Very simple problem: First model: I run a linear regression of $Y$ on $X$ and $Z$. Second model: I regress $Y$ on $X$ only, compute the residuals, and regress these residuals on $Z$. Why do I ...
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How to properly solve for the inverse problem of OLS? [duplicate]

In textbook ordinary least squares we want to find a vector of coefficients $b_{k+1\times n}$ such that the sum of the squared deviations of what's observed ($y_{n\times 1}$) from what's assumed to be ...
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1answer
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Power analysis for same model as “ANOVA” vs as “multiple regression” yields different results

I have seen posts that said ANOVA and multiple regression are theoretically the same. But if this is really the case, does anyone know why the G*Power (Linear multiple regression vs ANOVA) gives ...
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Fully connected layer vs Multiple parallel dense layers for multivariate nonlinear regression?

I'm trying to tackle a multivariate nonlinear regression problem that takes around 20 inputs and outputs around 200. I have a set of known points and need to come up with a performant neural network ...
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What are the advantages of linear regression over quantile regression?

The linear regression model makes a bunch of assumptions that quantile regression does not and, if the assumptions of linear regression are met, then my intuition (and some very limited experience) is ...
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2answers
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Do I need a validation set if I am doing 10-fold cross validation?

I am looking at a dataset with ~120 observations and I am investigating it using two sets of explanatory variables, one has about 12 features, the other about 8. This is for a regression analysis. ...
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Regression with non-unique values of dependent variable

I am wondering if I can estimate a regression, if the dependent variable y has duplicates, whereas all the independent variables (more than 15) are continuous and do not have any duplicates. In ...
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Sample Size: G*Power for hierarchical multiple regression with a three-way interaction?

I have been struggling quite a lot with finding a way to conduct a power analysis for a hierarchical regression with a three-way interaction. I will put 2 control variables in Step 1, 3 IVs in Step 2 ...
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Does multiplying a regression variable by a random variable with mean 1 affect the estimates

I'm dealing with a regression of the form $\log(Z)=\alpha\log(X) + \beta\log(Y) + u$, but instead of observing $Z$, I observe $Z'=aZ$, where $a$ is a random variable with mean 1. Does using these ...
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1answer
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Least squares regression coefficient with minimal information

If I only have a correlation matrix of 4 variables and the sample size, is it possible to predict 1 variables from the other 3 while using information about sample size? I’m trying to use lm but my ...
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relation between OLS regressions using different data transformations

I have a $(n \times d)$ panel $y$ of $n$ different variables , and a $(n \times d)$ panel $x$ of their forecasts. $d=$ time length of data $n=$ cross section width/ no. of variables I run a pooled (...
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1answer
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How to understand pvalue with controls/covariates

Suppose I have a study with a response variable $y$ and two explanatory variables $x_1, x_2$. I do a regression such as lm(y~x1) and get a p-value of $p_1'$ for $...
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Effect size in Negative Binomial Mixed Model

Is there a way to calculate Cohen's d (effect size) equivalent for a coefficient in level 1 (i.e., fixed effect) based on the output from a negative binomial mixed model (...
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Multiple regression including uncorrelated independent variables

I have two independent variables, one (variable-1) has a significant correlation with the dependent variable and the other (variable-2) does not. I want to first do multi-regression analysis (spss ...
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Regression using different data sets

Using a multiple regression, do all observations have to be from the same dataset? For example, assume a survey is conducted with some likert scale questions along with other predominantly categorical ...
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Type 1 Error correction for multiple comparisons: ANOVA vs multiple regression

After looking into Type 1 error correction protocols for multiple comparisons in ANOVA vs. MR, I found two (conflicting?) messages. The same Type 1 Error corrections that apply to comparisons in ...
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1answer
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Modelling binomial outcome in repeated measures design using glmer

I have a complex dataset for a repeated measures design. Each participant (N=53) saw a total of 72 images that varied according to three different properties (2 categorical and 1 ordinal independent ...
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Removing coefficients from multiple regression analysis

0verview I am undertaking a study where we analysing the fine details of two multiple regression equations. Multiple regressions were carried out for the months of February and August 2017, with ET ...
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1answer
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difference between interaction with anova and contrast functions

I'm trying to understand the difference between the interaction with the anova function and the interaction with the contrast ...
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How to do a sensitivity analysis on a non-linear equation?

In the company, it is very difficult to actually do quotations for our customers properly because we do not have perfect information regarding the factors that affect the cost and profit. So I created ...
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p value in backward elimination regression

I need some help with the backward elimination output from Minitab below. Can p values A, B, C, D be equal to 0.745? Or the p value should be smaller than 0.745?
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1answer
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Decomposing Historical Data - Arimax versus linear regression

In the creation of a "marketing mix model", past sales data, is regressed against various marketing spend (TV, radio, billboards etc) along with other aspects influencing a companies sales such as ...
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Linear regression when Y is bounded and discrete

The question is straightforward: Is it appropriate to use linear regression when Y is bounded and discrete (e.g. the test score 1~100, some pre-defined ranking 1~17)? In this case, is it "not good" to ...
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1answer
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Coefficient of multiple correlation for multiple linear regression with degree > 2 and interaction terms

I want to calculate the Coefficient of Multiple Correlation $R^2$ for a multiple linear regression with polynomial features of degree >= 2 (with interaction terms). Let's say I want to obtain the ...
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1answer
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Why do we use quadratic form for random vectors? [closed]

I am studying linear regression. I have studied this in the past, but this is my first time exposing myself to the matrix form of multiple linear regression. My matrix algebra/linear algebra skills ...
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How to interpret regression coefficients when each predictor variable contains different categories

Overview: I have conducted two types of statistical analysis using both linear regression and multiple regression. Overall, there were two observation periods, and the idea is to gauge if the rate ...
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Interpreting coefficients when variables are % of GDP and an index value (0 to 1)

My dep variable is investment (% of GDP) and my independent variables are saving (% of GDP), Terror (which is an index I have created, where a value of 0 is the lowest level of terrorism and 1 is the ...
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How to automatically identify degree of multiple independent variables of Polynomial Regression in R

In the dataset, there are 8 independent variable and 1 dependent variable. I want to use polynomial regression to find the relationship between independent variables and the dependent variable. The ...
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Whats the most appropriate test: Anova, multiple regression, or linear regression? Confused!

Overview As part of a group practical activity, we collected phenological data from deciduous oaks trees which were pooled into a large database (see the data frame below). Parameters Measured ...
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Presenting regression model

I have a problem with writing the regression model in my thesis. For example below; Fixed effects model with year,town and industry dummies. 1) How should I write the dummies in the regression model?...
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How to obtain regression coefficients of a multiple linear regression model from simple linear regression models? [duplicate]

Suppose I have a multiple linear regression model $$ Y=\beta_0+\beta_1X_1+\cdots+\beta_pX_p+\epsilon$$ How can I obtain the regression coefficients $\hat{\beta_i}$ by fitting just a series of simple ...
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What is the relationship between the standardized multiple regression coefficient & the semi partial correlation for models with k>2 predictors?

I have found myself Googling this question more than once: ¿What is the relationship between the standardized multiple regression coefficient (the standardized partial slope) and the corresponding ...
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2answers
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Linear Regression - holding predictor fixed at its mean

I am trying to create a linear model to predict House Price ($y$). The predictors in the dataset are Area (continuous) & Location (factor: West, Midwest, South, Northeast). I am asked to assess ...