# Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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### What is the 'right' slope formula of a regression? deltas or Pearson?

this may be a silly question, but still: I've been told that the slope formula equals the rise/run ratio, like this: $$m = \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_1}$$ in which rise equals ...
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### Testing equality of mean responses

In the context of linear regression, we know that $E(y|x_0)$ for a given new data $x_0$ is estimated by $\hat{y_0}=x_0^t\hat{\beta}$. If given another set of new observations $x_1$, is there a way to ...
1 vote
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### Counterexample where E(u|x)=0 in a regression model cannot hold in the population?

Edit: Background information: I have two variables of interest, $y$ and $x$ that are linearly related via the following: $y = a + bx + u$, where "$a$" and "$b$" are fixed ...
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### do you need to specify the direction of b for a moderated regression

I conducted a moderated regression, but didn't specify the direction of moderation by M. that is I didnt specify whether the relationship between X and Y would be greater at lower or higher levels of ...
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### Application of Maximum Likelihood estimation (MLE) to the step of Feasible Generalized Least Square (FGLS)

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
1 vote
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### Can we isolate the effect of two different control variables in a semi-partial correlation?

I know that we are able to use a partial correlation when we want to correlate X and Y but Z affects both of them and that we may use a semi-partial correlation when we want to correlate X and Y and ...
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### Approaches for running separate monthly regressions on a time series

I have a time series with daily granularity. The time series under consideration depends on an independent variable x (say). In order to account for seasonality effects - I run a separate regression ...
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### Logistic GLM vs GLMM diagnostic issues

Problem I am running through the diagnostics of two logistic regressions and two equivalent GLMMs with their only differences being crossed random effects (intercepts only). The output for the ...
1 vote
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### how well would a robust mixed model fit these data? R (rlmer)

I want to investigate Y ~ X1 * X2 + (1|ID on this dataset (there's a plot of these data in that post too, it's the same dataframe) Y is a continuos outcome ...
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### Change versus level regression

I tried running a panel regression of y on contemporaneous x variables, and again using the change in y from year t-1 to year t. I am getting the opposite sign on my variable of interest (VOI) if I ...
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### Regression on multiple variables as a whole and separately

I have been asked to predict the effect of Covid-19 on two variables as a whole and individually. The two variables are prices for commodities of two types. The data includes a daily record of prices ...
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### Conditional logistic regression for calculation odds ratios

I want to calculate the crude and adjusted odds ratios for exposure to occupational risk factors such as aluminum and fossil fuels in my case control study. My cases are 180 demented patients and I ...
1 vote
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### determining the effect of the change in an independent variable using regression

I'm creating a regression model that predicts a customer's spending based on their income, while adjusting for age, gender , and region. The model looks as follows: ...
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### How do Measure "Robustness" in Statistics?

I am an MBA Student taking courses in Statistics. Our prof was comparing two different methods of estimating the parameters for a regression model: General Method of Moments (GMM) and Maximum ...
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### Can we fit a regression model when the dependent variable is poorly correlated with the independent variables?

I have a requirement, I need to predict Y from 2 X_variables, I plotted two scattered plots ie Y vs X1, Y vs X2, As you can see the below pics, the plots are sparced. There is poor correlation between ...
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### separate models vs joint model

My goal is to estimate the association between children BMI and distance to the nearest fast food restaurants. The hypothesis is that children BMI increases with increasing proximity of fast food ...
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### Whether it is okay to dichotomise a 4-point Likert-scale outcome item

I'm using an already collected data-set within my research, meaning I was very limited with the outcomes that I could use. One of my two main outcome variables was an item using a 4-point Likert-scale ...
1 vote
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### How to learn steep functions using neural network?

I am trying to use a neural network to learn the below function. In total, I have 25 features and 19 outputs. The above image shows the distribution of two features with respect to one of the outputs....
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### References Request (Least-Squares Estimates for non i.i.d. Processes)

I am interested in suggestions concerning possible applications/problems within applied statistics with respect to estimates of least-squares for non-stationary designs. In particular, I would like to ...
1 vote
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### Standard error logic

Obviously the closer the standard error to zero the better. However, what if the values the in which the standard errors are from are extremely large and the standard errors are much higher than zero ...
1 vote
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### Robust standard errors with splines

I realize that large changes in model results between using robust and non-robust standard errors can suggest a misspecified model. My case refers to using a Cox regression and I have experimented ...
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### Time series to forecast a probability

I'm looking to forecast a time series, that is, forecast the next period give historical time series data. At the end of the day, what I want is to forecast a probability. The metric that I'm ...
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### Recommend a research-level book on econometrics, particularly for the theory of linear regression for random regressors X

Can anyone suggest a research monograph (with proofs or at least detailed references) for econometrics? Specifically, I'm looking to learn about the theory of linear regression and all the usual ...
In the second answer (https://stats.stackexchange.com/a/368426/287815) to the question (Why will ridge regression not shrink some coefficients to zero like lasso?), the OP found out that, $β = 𝑥𝑦/(𝑥... 1 vote 1 answer 15 views ### Derivation of factors associated with increase in HIV DNA I would just like to verify a statement made in the following paper: Peripheral blood HIV-1 DNA dynamics in antiretroviral-treated HIV/HCV co-infected patients receiving directly-acting antivirals The ... 0 votes 0 answers 35 views ### Are "Moments" More Robust Then "MLE"? I am an MBA Student taking courses in Statistics. We are learning about different ways to estimate the parameters (i.e. coefficients) of a Regression Model. Our professor indicated that there are two ... 1 vote 1 answer 391 views ### Assessing overfitting via learning curves I have intended to find overfitting or underfitting cases. I have used MLP classifier and Logistic regression of scikit-learn. How do I know which is a good fit? Or Which one underfitting or ... 1 vote 0 answers 30 views ### Is there a Relationship Between Variance and Chi-Square? I am an MBA Student that is taking courses in Statistics. Up until now, we had only encountered "Chi-Square" in the context of Contingency Tables. That is, how to find if the difference ... 169 votes 10 answers 193k views ### When is it ok to remove the intercept in a linear regression model? I am running linear regression models and wondering what the conditions are for removing the intercept term. In comparing results from two different regressions where one has the intercept and the ... 0 votes 0 answers 16 views ### How does an xtreg equation looks like? I ran some FE regressions in Stata using xtreg. One “normal” FE Model and a second generalized DiD Model. Now, I am wondering how the code would look translated into mathematical equation. Please ... 0 votes 0 answers 6 views ### linear regression removing interce [duplicate] I have 4 continuous x variables and it is a linear regression problem. I built the first model and recorded performance on the test data - Mean absolute % error. I also noticed that some x variables ... 0 votes 0 answers 6 views ### MLR OLS computing slope and intercept separately In multiple linear regression, when we want to derive the slopes and intercept separately, I have seen the following formulas:$\hat \beta = (X^T_c X_c)^{-1} X^T_c y_c\beta_0 = \overline y - \beta^...
We know that $\beta = (X^TX)^{-1}X^Ty,$ but when can we "distribute" the -1 in to get $(X^TX)^{-1}=X^{-1}X^{T^{-1}}$?