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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.

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Given m n-dimensional vectors, how to create a vector perpendicular to all of them?

Given $m$ vectors, $x_1$, $x_2$, ... $x_m$ with all $x_i \,\, \epsilon \,\, \mathcal{R}^n$, $i=1,2... m$ and $m < n$. How to sample a vector $x_{m+1}$ perpendicular to all the vectors $x_1$, $...
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How would I figure out - TSS of Y, Yi and XiYi from the following information?

I came across an analogous question when revising and have no clue how to approach it. The Given information is ΣXi= 20, ΣYi=40 Σ(Xi-x̅)²= 40, Σ(Xi-x̅)(Yi-nȳ)=20 and n=20. The question requires ...
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25 views

Validating a model built on multiple regressions

I have a program that models suspended sediment concentrations (SSC) using turbidity as a predictor and lab derived sediment concentrations as the response. The relationship between the two can ...
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7 views

Using a Linear Plateau Model

I want to see on which day injury healing plateaus using the following data (example): ...
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1answer
18 views

Logistic regression F value

I have a question that I’ve been struggling finding the correct answer to. I wonder if you can help? I am performing a logistic regression with multiple variables,only one variable is statistically ...
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18 views

Continuos variables described in one graph (cubic, quadratic, linear and logarithmic) [closed]

I want to illustrate the significance of the continuous variable "age" in one graph, both linear, quadratic, cubic, and logarithmic should be included. I think I have to compute a new variable with ...
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30 views

Parameters for regression linear model for two variables? [duplicate]

I made regression for two variables, one is independent (time of first pizza) and dependent (second is number of pizza that day). Trying to determine if there is connection between time of first pizza ...
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1answer
10 views

Analyzing multiple repeated measurements from same individuals under different conditions

I have 4 participants who are exposed to two different environments A and B and their skin temperature is measured every 10 minutes for 1 h. Hence there is 7 measurements per one experiment (0min, ...
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Can't find much online about “Linear Regression Estimators” — Looking for help making sense of notes on the topic

I have recently been lectured on how to implement linear regression estimators for a project I have going - I was walked through it works but I couldn't make sense of what was going on. See below for ...
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2answers
671 views

What is the problem with $p > n$?

I know that this is the solving system of linear equation problem. But my question is why it is a problem the number of observation is lower than the number of predictors how can that thing happen? ...
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significance in linear regression with constraints

I have a problem which is similar to linear regression, but differs in two main points: 1) the number of regressors is equal to the number of observations and 2) I have constraints on the regressors. ...
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Linear independence [migrated]

In my mind there is a conflict between the "intuitive" definition of linear dependence of vectors i.e., that : $\vec{v_1}=k\vec{v_2}$ and the formal definition that says that there must be at least, ...
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Quasi-likelihood Estimation and Linear GEE

I am trying to better understand some of the assumptions of the estimator I am using, which is linear GEE. It is my understand that linear GEE uses quasi-likelihood estimation and so it has weaker ...
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1answer
13 views

Does 0-sum game violate linearity in linear regression? [closed]

I have a dataset that is derived in the fashion of 0-sum game (RNA-Seq data: the total amount of reads is fixed, inclusion of one read belonging to one feature means the exclusion of another read ...
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22 views

Residualizing in OLS

Consider a linear regression $$ y_i = A_i' \theta + B_i' \psi + \epsilon_i $$ There's a "trick" to find the parameters $\theta$ and $\psi$ in a stepwise fashion. First minimizing squared error wrt....
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42 views

Data Transformation to achieve Linearity

One assumption of OLS regression is Linearity. To check whether the assumption holds, you can plot component + residual plots or partial residual plots. When a linear relationship is apparent, is's ...
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1answer
39 views

Linear regression - Can I log transform dependent variable and one of the independent ones and keep the rest not transformed? [duplicate]

I have model where my dependent variable is Total money spend and then I have independent variable Income and some other ...
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1answer
80 views

Why does Covariance measure only Linear dependence?

1) What is meant by linear dependence? 2) How can I convince myself that covariance measures linear dependence? 3) How I can convince myself that non-linear dependence is not measured by covariance?...
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1answer
32 views

How to standardize count data for different sampling site sizes

I want to do a linear regression for my data but I’m not sure what I need to do with my raw data before running a linear regression. I have counts for species in several forests of differing sizes. I ...
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42 views

Why is regression line represented as $y = b0 + b1 * x$?

I am new to Data Science and ran into Regression Line formula which is $ y = b0 + b1 *x $ (where x is dependent variable, y is predicted variable) I understood the meaning of this formula as a ...
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2answers
22 views

Random intercept in mixed model w/ post baseline measurements

I'm running a LMM analysis for a clinical trial (two treatment conditions, five visits) and I can't understand the exact role of a random intercept. The baseline score is not included in the outcome (...
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0answers
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What is a good model for learning power equation against frequency for a chip

Here's my problem scenario:- I have to come up with a power equation as a function of frequency. The plot fits well with a higher order polynomial (4th or 6th) :- $$Power = \theta_0 + \theta_1 fr^1 + ...
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1answer
31 views

Combing logit and linear regression

I am looking for a proper method for my research. I want to analyze left-right political position of a person. My idea is to combine logit regression with a linear regression. Logit will decide on ...
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What is prediction in PRF exactly? (Regression Question Series - Part 5)

Preface: This is slightly alternate question from previous question here. It arose because I find difficulty grasping the basics of regression still (sure, I am doing multiple revisits to basics again ...
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1answer
40 views

How to implement topic modelling in regression analysis

I have a dataset consisting of hotel reviews, ratings, and other features such as traveller type, and word count of the review. I want to perform topic modeling (LDA) and use the topics derived from ...
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23 views

Characterizing estimator, estimate and RV (Regression Question Series - Part 3)

Given a sample set $(X,Y)$, supposing $X$ is fixed and known, Population Regression Function,PRF: Hypothesizing the underlying population, we have, $$\begin{aligned} & E(Y) = \beta_0 + \...
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22 views

Interpretation of correlation in endogenous regression model

Suppose you have a linear regression with an endogenous regressor $x$ that can be represented as follows: $x = z'\delta + \epsilon_1$ $y = \beta x + w'\gamma + \epsilon_2$ where $\begin{pmatrix}\...
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Is residual in a SRF, an estimate of error in PRF? (Regression Question Series - Part 2)

PRF: Given a sample set $(X,Y)$ we hypothesize underlying population has a regression line as follows. \begin{aligned} & E(Y) = \beta_0 + \beta_1x & \scriptsize \text{(1) PRF} \\ &...
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2answers
26 views

Statistical measure for linear regression with two distinct clusters of points

In the following plot, I have a linear regression of 30 points, representing 10 treatments with three replicates each. As you can see, the r-squared value is quite strong (0.83) and the p-value is ...
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36 views

Linear least squares algorithms

I have stumbled across these two questions and accepted answers: (1) Do we need gradient descent to find the coefficients of a linear regression model? (2) Why use gradient descent for linear ...
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1answer
188 views

Which is the dependent variable?

I was looking at this Data Science question on TestDome. The problems is stated as the following: Implement the desired_marketing_expenditure function, which returns the required amount of money ...
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1answer
21 views

Linear regression of dependent variable squared & retransformation

I have performed linear regression of a dependent variable squared, & my statistics package produced least squares means for each level of categorical variables that I would like in original units....
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33 views

What is the difference between taking a transformation of a response variable to then apply linear regression and a GLM? [duplicate]

From what I've studied so far, GLM's are to be used when the error term of a response variable is not assumed to be normally distributed. However, I also read that sometimes a transformation of a ...
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1answer
23 views

Converting relative effect to absolute effect in log model

I have the following model; log(daily sales) = intercept + B1*(event dummy) + error My response variable(daily sales) is basically a daily time series and 'event dummy' is an indicator variable ...
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Scale-Location Graph question

This graph is confusing me. I am assuming there is no equal variance because the residuals are spread out so much; however I am not sure. Please verify this for me.
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Pearson and R^2 Correlation between three variables

Get it from someone else but don't quite know how to answer. If $\rho_{X,Z}=0.4$, $\rho_{Y,Z}=0.3$, what is the range of $\rho_{X,Y}$? Here $\rho$ is the Pearson correlation coefficient. We run a ...
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14 views

Linear Unconditional X-Y, Non-Linear Conditional X-Y

Intuitively, I can imagine that an unconditional (i.e., unadjusted for any covariates) Y~X relation can present as a linear relation, whereas a conditional Y~X|Z relation can present as a non-linear ...
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linear graph for 2 datasets one with 100s legend and the other with millions

I ran into an issue that I have to display the correlation between 2 lines in 1 graph chart, the problem is 1 line values are within hundreds, the other line values are millions. I do not care about ...
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63 views

Linear Regression Using a Variable and Standard Deviation of the Variable

UPDATED: Sorry for the confusion! I changed parameters to regressors, and added in example data (not real data). I am currently doing something like Day ~., but using ANOVA to find the best regression ...
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2answers
19 views

Unsupervised Classification of Linear Trends

I have a data set which results in a series of non-parallel linear trends on a scatter plot. I'm trying to find a way to classify each data point into its closest corresponding linear trend. There ...
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Proving that $V(\hat{y}_{x_0}) = \sigma^2\bigg[\frac{1}{n}+\frac{(x_0-\bar{x})^2}{S_{xx}}\bigg]$ [duplicate]

Exercise : Prove that the variance of $\hat{y}_{x_0} = \hat{b_0} + \hat{b_1}x_0$ is : $$\text{Var}(\hat{y}_{x_0}) = \frac{\sigma^2\sum x_i^2}{n\sum(x_i-\bar{x})^2}+\frac{\sigma^2x_0^2}{\sum(x_i-\...
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2answers
81 views

Showing that $\sum_{i=1}^n (y_i-\hat{y_i})(\hat{y_i} - \bar{y}) = 0$ for the generalized linear model [closed]

Exercise : Prove that for the generalized linear model, it is : $$\sum_{i=1}^n (y_i-\hat{y_i})(\hat{y_i} - \bar{y}) = 0$$ Question : How would one proceed with proving that for the generalized ...
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2answers
61 views

Degrees of freedom for linear regression

I'm reading on a text book about linear regression, and when I thought I finally understood degrees of freedom, I found a statement that made me doubt what I know so far. Well it's in the context of a ...
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0answers
26 views

Converting linear variable's coefficient to log scale

I have a linear regression model with some variables log transformed: Y = Beta1.Log(X1) + Beta2.Log(X2) + Beta3.X3 Y is a percentage variable (A credit card companies market share) and X3 is Premium ...
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0answers
41 views

Linear Prediction and Linearity of CEF

I am revisiting the basic notions of linear regression and stumbled upon the following idea in Cameron and Trivedi's Microeconometrics book: However, for the conditional mean to be linear in x, so ...
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1answer
56 views

Functional form of f

I am reading An Introduction to Statistical Learning with Applications in R by G. James, D. Witten, T. Hastie and R. Tibshiran 2013 after taking a basic statistics course a little while ago. On ...
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1answer
32 views

How can I remove the effect of one independent variable so I can standardize and compare the values of my dependent variable?

I have a table of television viewership data with each row being one series and the columns being various data about that series, e.g. name, time the series is on TV, length of an episode, how many ...
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42 views

Produce MSE by using cv.glm() in multiple linear regression, how about a transformed y variable

I applied 10-fold cross validation by using cv.glm() function in the linear regressions. I am able to obtain the MSE in this way, mse=cv.glm(data,model,K=10)$delta However, if I applied ...
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25 views

Linear Regression Coefficient changes with additional variables

Folks, In linear regression, I am looking to understand why the coefficients of a given independent variable (HS_ENGL in this example) would change as other independent variables are added (SAT_VERB ...
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69 views

How do you prove $E(\text{MSPE})=\sigma^2$

I started with: $$E(\text{MSPE})= E\big(\text{SSPE}/(n-c)\big)= E\bigg(\sum_{i=1}^{c}\sum_{j=1}^n(y_{ij}-\bar{y_i})^2/(n-c)\bigg),$$ but I am not sure where to go from here.