Questions tagged [linear]

For statistical topics which involve the assumption of linearity, for example, linear regression or linear mixed models, or for the discussion of linear algebra as applied to statistics.

Filter by
Sorted by
Tagged with
0 votes
0 answers
11 views

Would the Mantel-Haenszel test for linear trend be appropriate for this data/hypothesis?

I am testing whether or not there is an association between the parents education level and the pupils grades in the oral exam in social studies in the last year of danish primary school from the ...
user avatar
  • 1
0 votes
0 answers
31 views

Why is total variation $\sum_{i=1}^{n}\left(Y_{i}-\bar{Y}\right)^{2}=\sum_{i=1}^{n} y_{i}^{2}$? [closed]

I've been interested in Econometrics and the book I use is Econometrics by Badi H. Baltagi, 5th edition. I tried to answer some of the problems. However, one problem from chapter 3 no. 2 got me ...
user avatar
0 votes
1 answer
43 views

What does it mean if my confidence interval includes zero with a significant p value in linear regression analysis?

I performed linear regression analysis to assess the associations between continuous variables. I found a significant p-value but my confidence interval includes zero. What does it mean? Here are the ...
user avatar
  • 51
3 votes
0 answers
35 views

Gauss-Markov with $p>n$

Let $p$ be the number of parameters in a linear regression model, let $n$ be the number of observations, and let $p>n$. $$\mathbb E[Y\vert X] = \beta_0 +\beta_1X_1 +...+\beta_pX_p$$ Does the Gauss-...
user avatar
  • 30.9k
0 votes
1 answer
39 views

Multiple linear regression: Do all independent variables need to have good adjusted R-squared independently?

I'm very sorry if this should be obvious, I'm just feeling a little lost with this assignment.. I have four independent variables X1,X2,X3,X4 plus a constant, modelled against Y. I know X4 to be ...
user avatar
  • 1
1 vote
0 answers
22 views

How to compare the goodness of fit between linear and logit? Why linear deviance is less than logit?

How can I evaluate which model - between linear and logit - determine the best fit to the data? The models use the same input variables and I thought that comparing the deviances was the proper choice ...
user avatar
0 votes
0 answers
8 views

Biased, linear MMSE estimator from biased measurement data?

I am trying to find out if what I am looking at is a known problem. I am considering the case of weighted least squares, and I am trying to find the optimal weights of biased measurements. I have ...
user avatar
  • 101
1 vote
0 answers
19 views

Question about confidence interval and standard errors on graphs

So I made a graph in R, it’s a linear regression of the same sample at different concentrations. It has a confidence interval built into it of 95%. Then I had to determine the concentration of an ...
user avatar
  • 11
0 votes
0 answers
20 views

which model should be used for calculate the residuals of DV in twin data

I want to use the residuals of the dependent variables as new variables for analyses. these variables are continuous mammographic density measures from twin data. so which model should I use for ...
user avatar
  • 101
1 vote
1 answer
46 views

Linear Regression with Lasso Regularization by using scikitlearn and scipy.optimize

i am trying to apply lasso linear regression with both scikitlearn and scipy.optimize min method. However, i cannot reach same result. Code that i created with scipy.optimize can't shrink redundant ...
user avatar
1 vote
1 answer
16 views

Comparing Activities with regression

I am trying to find out what is the effect of activities(like jumping, weight lifting etc.) on behavior (such as attitude towards participating in a marathon). (sample size of 60 observations for each ...
user avatar
  • 11
1 vote
0 answers
19 views

Show that hypotheses $A\theta_0=c$ and $\theta_0=B\delta_0+e$ are equivalent

I am working on a following task. Let $A\theta_0=c$ where $A$ $(q \times d)$ and $c$ $(q \times 1)$ are known with rank $r(A)=q$. Show that the former linear hypothesis is equivalent to $\theta_0=B\...
user avatar
  • 111
5 votes
2 answers
680 views

Correct formula for MSE

Throughout my student life so far, I have always considered the mean squared error to be calculated by $ MSE=\frac{1}{n}\sum(Y_i-\hat{Y}_i)^2$. However I was looking at one of my statistics mod today ...
user avatar
  • 167
0 votes
0 answers
17 views

matrix result needed to show consistency of equation

I am trying to show the following system of equation Va+Xb=0 and X'a=k, is consistent when a'X=k', where V is nXn and X is nXp (p<n) matrix, a,b,k are vectors. I could not find the reason how Va ...
user avatar
1 vote
1 answer
39 views

Is Ordinal logistic regression linear or nonlinear?

Quick question, is ordinal logistic regression a linear or nonlinear model? Finding different sources supporting the other, and the more I read the more I get confused myself. Perse, it should fall ...
user avatar
0 votes
0 answers
15 views

Regression - fitting with linear combination [duplicate]

Consider a linear regression model with two regressors x1 and x2. Suppose, I fit a new model with regressors x1+x2 and x1-x2. Are these two models equivalent? What is the relationship between the ...
user avatar
3 votes
1 answer
65 views

E(log(x)) to E(x) [duplicate]

Sorry if this is a straightforward question, but I have tried digging into econometrics book and cannot find anything about it. I worked on a model with ...
user avatar
  • 41
0 votes
2 answers
43 views

How do you create a linear regression formula from the results of a summary in R?

Say you have: data.lm summary(data.lm) It prints out: ...
user avatar
0 votes
1 answer
47 views

Why Generalized Least Squares?

So it is often advise to use Generalized Least Squares when we have a regression model with non-spherical(i.e. heteroskedastic or autocorrelated) errors. We do so by doing a weighted regression $$ (y-...
user avatar
  • 101
2 votes
0 answers
10 views

Finding linear relationship between A, C using known linear relationships of A, B and B, C?

I have three tests A, B, C. I have many samples of students who have taken tests A and B and, using linear regression, have found a relationship between test scores of A and B. Similarly, I have many ...
user avatar
1 vote
1 answer
19 views

why diagonals in a pair plot is a histogram instead of line plot?

why do diagonals in a pair plot is a histogram instead of a line plot? Doesn't it make sense to have a line plot with the 45-degree linear line passing through the origin? This is a general question ...
user avatar
0 votes
1 answer
19 views

When to what when building a linear model?

There a many tools to building linear models, such as adding non-linearity, adding splines, adding interactions, variable selection. It can feel overwhelming when considering all of the options… For ...
user avatar
  • 1
0 votes
0 answers
22 views

Linear transformation between two multivariate normal distribution

Suppose I have two multivariate normal distribution $N_1$, $N_2$. If I know the mean and cov of $N_1$, $N_2$:$\mu_1$, $\Sigma_1$, $\mu_2$, $\Sigma_2$. Can I find a linear transformation which makes ...
user avatar
1 vote
0 answers
8 views

Regression lines and dependent variables [duplicate]

I have seen several practice questions using a simple linear regression eg y = ax + b where the question indicates that using a supplied value of y to find the x variable is invalid because the ...
user avatar
  • 11
1 vote
0 answers
24 views

Which ML method should I use to make a prediction function for accident data?

I have road accident data from 2000 to 2020 with counts divided into categories like "Junction Type" etc.? I want to build a prediction model using ML, So which technique should I use Linear ...
user avatar
1 vote
1 answer
33 views

Interaction between quadratic term and dummy variable

Suppose I have a linear regression: $Y=\beta_1+\beta_2X+\beta_3X^2+\beta_4D$ where $D$ is a dummy variable that takes value 0 and 1. If I want to examine if the effect of $X$ on $Y$ for $D=0$ and $D=1$...
user avatar
  • 13
0 votes
0 answers
13 views

Discrepant results: tau coefficient and linear regression

I have two continuous variables $x, y$ that are not normal, but whose logarithmic transformations are normal and meet all assumptions for linear regression. In R, I evaluated their correlation through ...
user avatar
  • 101
0 votes
1 answer
22 views

How can I perform linear regressions on data that does not respect application conditions for parametric application

I'm trying to determine if different linear regressions are statistically different from one another. For that, I used the regression function for my different treatments (round, triangle and square ...
user avatar
2 votes
1 answer
36 views

A post-hoc test for linear regressions with interaction?

I've been looking for an answer for a question (which I thought was rather trivial) for a while now, but can't seem to get the correct solution for it. I'm working on data of blood parameters (e.g. ...
user avatar
  • 25
1 vote
0 answers
16 views

Degrees of Freedom for Linear Combination of Variables

I have three mean estimates, all from variables assumed to follow a Normal distribution. The following is a mock example. x1 is estimated at 4, with a standard error of 5 and 6 degrees of freedom x2 ...
user avatar
0 votes
0 answers
33 views

Advice on best technique to compare data to a horizontal line with slope = 0?

I have run into some difficulties figuring out which statistical test is best to use in the following scenario: Consider a typical line y = mx + b For a given domain on a plane, say 0 to 1, I have a ...
user avatar
1 vote
0 answers
19 views

State space model equation

I would appreciate your help on the following I have a quadratic equation and need to write it in a state space format according to a model below. My equation is the following below, where T is the ...
user avatar
  • 11
2 votes
1 answer
48 views

Is cross-validation necessary when computing significance of coefficients?

I'm unclear on if its important to perform cross-validation when determining if a dependent variable has a significant effect on my independent variable in multilinear regression. Specifically, I'm ...
user avatar
  • 23
0 votes
0 answers
5 views

References for interpretation of residual errors on log log regressions

In a paper I'm writing, I'm interpreting the residuals on my log log regression as approximating relative error. I have a (fairly simple) proof that this is valid (for small residuals). I was just ...
user avatar
0 votes
0 answers
8 views

What feature or property of multiple linear regression makes it to distinguish between important predictors vs non-important predictors?

In the Introduction to Statistical Learning, in chapter 3, a linear regression problem is discussed. The problem is to discover the relationship between sales and advertising on three media (TV, Radio,...
user avatar
  • 143
2 votes
3 answers
73 views

Can we use $y * \operatorname{sgn}(\hat y)$ as a loss function in linear regression?

Can we use $y * \operatorname{sgn}(\hat y)$ as a loss function in linear regression where $\hat y$ is the prediction and $y$ is the target value, or is there any other loss function close to this ...
user avatar
2 votes
2 answers
78 views

the two step approach

I have a continuous variable which is not normally distributed i want to transform it to normal using the two step approach method in the link below: Abstract This article describes and demonstrates ...
user avatar
  • 57
0 votes
0 answers
18 views

Linear or quantile regression to deal with leverage points?

I'm doing a linear regression model, but even after the log-log transformation it contains many leverage points (outliers that are part of the data), the residuals are not normal and the variance is ...
user avatar
  • 5
0 votes
0 answers
17 views

How does one calculate the significance of the coefficients of a linear regression? [duplicate]

When I run a linear regression in the form of $y$ = $\hat{β}_0$ + $\hat{β}_1x$, I not only can calculate the values and SE of $\hat{β}_0$ and $\hat{β}_1$, but also their z-scores. Now what I don't ...
user avatar
1 vote
1 answer
57 views

Calculating Slope and Intercept From Multiple Linear Regression

Consider this linear equation: $$ Y \sim \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \beta_4(X_2*X_3) + \epsilon $$ where $Y$ is what I'm trying to explain (it happens to be the evolved growth ...
user avatar
1 vote
1 answer
32 views

Relationship of covariance and linear regression in context of rank deficiency

Beforehand Usually, we can get intercept and slope of a linear regression from numbers we get from a covariance analysis of same variables. This goes like this: ...
user avatar
0 votes
0 answers
16 views

Arrange data so that two variables are linear

I have the following set of rainfall intensity data and I want to make a compilation of the rainfall intensities above some practical minimum as shown in the figure below. So the intensity and the ...
user avatar
  • 1
0 votes
1 answer
49 views

Linear Regression of non-normally distributed data [duplicate]

I am trying to understand the relationship between royalties received (independent variable) and health expenditures (dependent variable) for each municipality through a linear regression. My ...
user avatar
  • 5
6 votes
2 answers
560 views

Simple linear regressions among three pairs of variables

Let the "ordinary-least-squares regression of $Y$ on $X$" be given by $$\hat{y}_i = \hat{\beta}_0 + \hat{\beta}_1 x_i\text{.}$$ Suppose I run the following: The OLS regression of $Y$ on $X$ ...
user avatar
  • 3,883
1 vote
1 answer
23 views

Correcting A Raffle Problem

An interesting scenario that I'm trying to wrap my mind around. Let's say you were running a giveaway, and have a probability of 10% for every participant to potentially win a prize. The way you would ...
user avatar
0 votes
0 answers
9 views

Is it possible to run a multiple linear regression analysis when one of the categorical predictors has more than 2 groups? [duplicate]

I want to run a multiple linear regression analysis with 5 categorical or continuous predictors (independent variables) for a continuous outcome (dependent variable). Is it possible to use a multiple ...
user avatar
  • 41
0 votes
0 answers
53 views

Does the variance of the regression coefficients in simple linear regression always decrease when sample size increases?

As the title says, I am wondering if the variance of the regression coefficients (intercept and coefficient of x) always decreases with an increased sample size. I managed to figure out that the ...
user avatar
1 vote
0 answers
16 views

References on the non-decomponition of linear correlations

Given $a, b, c, d$ as numeric vectors of the same lenght (e.g. 2), and $\phi$ being a measure of linear correlation (e.g. Yule-Pearson correlation = Matthews Correlation Coefficient), I would like ...
user avatar
0 votes
0 answers
18 views

Statistical difference between linear data sets

I am conducting a project where I am looking at how the status of a hydraulic filter can be determined using only the hydraulic motor current and load pressure. Plotting the data with current as the ...
user avatar
1 vote
0 answers
15 views

Linear Regression Model Selection [duplicate]

I know that a useful method is to see the AIC or nested F-test but... is it correct to select variables with the stepwise methodology, selecting the variables with the lowest p-value from the t-test ...
user avatar

1
2 3 4 5
26