multiple-regression's questions - English 1answer

3.240 multiple-regression questions.

Let's say $x$ is correlated to both $y_1$, and $y_2$. Why are the residuals of the nested regression of $x$ against $y_1$ and $y_2$, not equal to the residuals of the simultaneous (multiple) ...

I am trying to fit the following linear model: ...

I'm working on the following linear model - y ~ x1 + x2 + x3.....where y is number of cigarettes smoked. Suppose the observation is such that they smoke 40 cigarettes. How would I calculate the ...

I have a question about the package leaps which I am using for model selection. I would like to compare 4 different selection methods: forward, backward, stepwise and best subset. I used the code ...

I am quite new to Machine Learning and come from a computing background. I have a quite big set of features (~50) with about 4k observations. Is it correct thinking to include all of them in a ...

In my research I'm looking at the correlation between self-harm and aggression (both continuous). Now, I also have some variables (e.g. depressive symptoms; also continuous) which I do believe ...

I used the PROCESS macro for SPSS from hayes to regress a model where det_mean is the indepedent variable and y_tot the depending variable. I'm testing if this relation is moderated by two variables ...

I am trying to get some intuition around regression when the data matrix $A$ is not full rank in the following regression/least squares problem: $$y=Ax+b$$ where $y \in \mathbb{R}^n$, $A \in \mathbb{...

I am wondering if Point Biserial Correlation is applicable for multiple binary independent variables and a dependent count variable. I have read how it was derive for a two variable system of one ...

I'm trying to understand why centering myregressor at a nonzero value improves the performance. I always thought that the variance of the feature, and its correlation with the labels, would affect ...

I have a linear regression model: $Y~X_1+X_2+X_3+X_4+X_5+X_6+X_7+X_8+X_9$ and I need to create a function that find all possible models (e.g. $Y = X_1+X_2+X_3+X_4$ $Y = X_2+X_3+X_4$ $Y = X_1+X_3+...

In a regression analysis, we aim to find the best relationship between two variables (independent variable denoted $y$ and other dependent variable denoted by $x$, and which are related by: $y = f_\...

I am looking to run regression using a variety of predictor variables: Chemical exposure (1 or 0) - variety of chemicals but all are binary predictors, Illness diagnosis (1 or 0), and TBI severity (0 ...

I have a vague memory that this relationship is possible, but I can't think of any examples off the top of my head. Is there a canonical or common example(s)? I am imagining that in two independent ...

I'm running multiple linear regression with 6 variables. For one of the variables D, the correlation coefficient between D and the response Y is - 0.34. But in the regression output, the coefficient ...

I have conducted a parametric study and have obtained a dataset. $Y$ is the independent variable and $X_1$, $X_2$ and $X_3$ are the three independent variables. Now, looking at the problem, I felt ...

I am dealing with a noisy dataset that has a certain amount of error for every estimator. Say, xi's are plus/minus a constant. I am wondering if there is a way to handle these errors or at least see ...

I plan to build a dynamic regression model with weekly sales data over a three year period (Jan 2014-Dec 2016). The three series are sales, price and advertising spend. I have complete data for all ...

I'm trying to forecast out sales in 2019 using significant independent variables, however these are mostly, if not all, unknown. The method I'm currently using is to use excel "forecast" function to ...

I have two studies, let's call them A and B. Both involve fitting a linear mixed model on what is essentially the same type of data; the two studies differ in only small ways. In A I found a ...

Will there be any issues related to degrees of freedom if we consider data for just 6 countries from time period 1980-2015?

I'm looking for answer for the question about multivariate polynomial regression. I can't find a clear explanation of when an interaction term is necessary. Some sources say that the estimated model ...

I am trying to use a combination of binary and continuous input variables in a linear regression. In my studies I used only continuous variables in linear regression. Should I do anything special ...

I believe the rule of thumb is at least 10-20 observations per predictor variable, but I was hoping to get some additional clarification. Suppose a hypothetical example with dependent variable of ...

I want to use a Difference-in-Difference approach. In order to make sure treatment and control group are similar, I want to use a propensity score matching before the DiD approach. What I do is to ...

I have took a look in a video that the guy was doing a regression analysis for forecast sales. He has a dataset with two columns (date and sales, for the past). He made a transformation on the ...

Hopefully somebody can help me or point me in the right direction! I've done a study comparing the effect of a training on a continuous dependent variable, let's call it symptom severity. The study ...

What is a suppressor variable in multiple regression and what might be the ways to display suppression effect visually (its mechanics or its evidence in results)? I'd like to invite everybody who has ...

I have a D-W = 1.312 with a sample of 22 cases. Is it a good value for running a multiple linear regression model?

This question is regarding the use of imputation methods, such as Multiple Imputation, for multiple regression models. It is often suggested that one should compare the regression model created using ...

Please I am exploring for multicollinearity in my data between socio-economic characteristics. I ran a collinearity diagnostic test and I have a conditional index of 6.235 which is less than 10. I ...

I have trained a linear regression model, using a set of variables/features. And the model has a good performance. However, I have realized that there is no variable with a good correlation with the ...

Assume that the true (but unknown) relationship in a population between $Y$ and $X1, X2, X3, X4$ is $$Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_4 X_4.$$ Further assume that I have a ...

Methodological question in preparation of an experiment with 4 groups of 10 growth chambers each. It is hypothesized that parasite infestation will affect growth chambers climate, as measured hourly ...

While researching OLS, I found out the equation to calculate coefficients as: $$ \beta = (X^\top X)^{-1}X^\top y $$ (Ref: https://en.wikipedia.org/wiki/Linear_least_squares) However it does not ...

I was asked to do a correction of p-values for my analyses, but I'm not sure what p-values I am to correct, and presuming I'm using Bonferroni, what is the number that I am dividing the .05 level with....

I am studying the factors influencing the annual salary for employees at a undisclosed bank. The regression model that I have decided to employ is as follows: \begin{equation} Y_{k}=\beta_{1}+\beta_{...

If an existing questionnaire does not exist to tap into a construct, is it better to change the instructions of a preexisting measure that isn't quite tapping into the variable of interest to have ...

Basically I want to know how the 'constant' value differs in each of the following models: Model 1: DV=income; IV1=gender (0=male, 1=female); IV2=location (0=east, 1=west) Here, I understand the ...

Is there any literature, examples, advice, etc. out there on creating real-time detection algorithms from a multivariate longitudinal block-design experimental data? (same 5 variables being collected ...

I'm aware of the formula for univariate linear regression. Can you share any similar equation for regression with more than one independent variables?

When performing a general linear hypothesis test using the glht function within the R multcomp library. For example: ...

Consider the linear regression model $$y_t = \beta_1+\beta_2x_{t1} + \beta_3x_t2 +u_t.$$ Rewrite this model so that the restriction $\beta_2 - \beta_3 = 1$ becomes a single zero restriction. ...

I'm currently working on building a predictive model for a binary outcome on a dataset with ~300 variables and 800 observations. I've read much on this site about the problems associated with stepwise ...

I want to run a time series regression over data is not spaced out in regular time intervals and where in some time periods there are multiple observations. Such in the picture below. Is this ...

Consider the linear model estimated by OLS: $$ y = X\hat{\beta} + \hat{u} = X_1 \hat{\beta}_1 + X_2 \hat{\beta}_2 + \hat{u} $$ We say that the above equation is the long regression, Consider also ...

I am using OLS to estimate the effects of various factors on the sales of different items. The data are monthly, and vary somewhat in the number of monthly observations available (some of the items ...

tl;dr: linear model is better than ANN and decision tree in timeseries regression task, why is that? I have a time series dataset of 151 observations each with 43 macroeconomic variables. Some of the ...

I am measuring the proportion of different types of bacteria killed by 4 different antibodies (simplified for illustration) ...

I have a theoretical economic model which is as follows, $$ y = a + b_1x_1 + b_2x_2 + b_3x_3 + u $$ So theory says that there are $x_1$, $x_2$ and $x_3$ factors to estimate $y$. Now I have the real ...

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