Refers to any model where a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.

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1answer
39 views

How to emphasize on specific data points in Linear Regression?

I'm now solving linear regression problems. $y = wx + b + e$ So I have $(x, y)$ data set and want to learn weights $w, b$. Additionally I know that certain data points are not polluted by noise ...
0
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1answer
19 views

Statistical independence of least square estimator and residual in multiple linear regression

I'm currently self studying linear regression. Following is an entrance exam problem of a graduate school. Consider the regression model with usual assumptions of the errors $y=X\beta+\epsilon$. Show ...
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1answer
32 views

Material difference between Mixed Effects Model and normal Linear Model

I have a question about normal linear models vs mixed models. Say I'm predicting prices for certain products, and I know two things: store and brand: In a linear model (lm), this would be: ...
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0answers
32 views

Asymptotic distribution of $\hat{B_1}$in simple linear regression

I am currently studying how to $\bf{identify}$ the parameter $B_1$ in a simple univariate regression model where we have $Y=B_0+B_1X+\epsilon$ with the usual assumption of $X$ being exogenous, ...
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0answers
18 views

How do I obtain the slope and intercept for each regression with a 2-level factor?

Suppose I have a data frame that include a factor with two levels. The response is proportional to the predictor, but the slope depends on the factor: ...
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0answers
24 views

Explanation of the formula for calculating adjusted R squared of linear model

The classcial formula for calculating the adjusted $R^2$ of a linear model is as follows: $$R^2_{adj} = 1 - ((n-1)/(n-p-1)) \times (1-R^2)$$ where $n$ is the sample size and $p$ is the number of ...
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0answers
8 views

Perturbation of variables in multiple linear regression

I have a linear regression problem on the form $$ y = \beta_1x_1 + \beta_2x_2^2 + \varepsilon, $$ where I've fit a model, so I have the regression coefficients $\beta_1$ and $\beta_2$. I would ...
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2answers
25 views

White Test , testing for heteroscedasticity

i used a White Test for testing the homoscedasticity assumption of my linear regression I am working on. I have a problem whit the interpretation as I have a result from the test in which the p-value ...
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0answers
20 views

ANCOVA; CIs for the intercepts of each treatment

I am currently doing an ANCOVA, and I need to calculate CIs for the intercepts of each treatment (categorical) group. So, instead of using lm(y~x+group), which gives me SEs of treatment contrasts, I ...
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0answers
14 views

Corner-point constraints

Can someone tell me a reference for the following issue, or just explain this to me: I understand what the corner-point constraint is in linear models, but I would like to know the origin and meaning ...
0
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1answer
30 views

NA values in linear model in r

I have the following dataset: desingmatrix <-read.csv("path of csv with data", sep=";", dec=".") View(desingmatrix)# vision de los datos Then I try to set ...
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0answers
5 views

ESL: base error rate question

In page 51, of ESL, it says "The mean prediction error on the test data is 0.521. In contrast, prediction using the mean training value of lpsa has a test error of ...
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0answers
19 views

Regression on beta coefficients from different models

Brief Background: Let's say I performed different regression models and found their beta coefficients estimates with their corresponding variances. I would now want to do a regression on those beta ...
1
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1answer
43 views

In absence of a constant, no need for $Cov(Y_i,\epsilon_i)$ just $E(Y_i\epsilon_i)$

We have the following simple linear model: $C_i=kY_i+\epsilon_i$, where $\epsilon_i$ is the error term. In a book I'm reading, the author states that due to the absence of a constant, we do not ...
4
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1answer
50 views

Testing a regression coefficient against 1 rather than 0

Brief caveat- I haven't dusted off my stats knowledge since some university courses a few years ago, and I'm struggling with cobwebs. I have a model where a linear 1 to 1 relationship has been ...
3
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1answer
48 views

Intuitive meaning of error-in-variables

I understand the explanation of the example of error-in-variables used wikipedia. What I do not understand is how could we explain intuitively the error-in-variables problem? One way would be to say ...
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0answers
29 views

In linear model, if you add one more variable, then what happens to the constant?

I have a linear model $$y=a+bX_1+cX_2+dX_3+eX_4+m,$$ where the expected value of $m$ given $X_1,X_2,X_3,X_4$ is zero. If you add one more variable $X_5$ to this model, is the constant $a$ expected ...
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0answers
9 views

Is there some analysis of block-greedy algorithms for feature selection or sparse approximation?

I consider the problem of sparse approximation, where one has a signal $\vec y = \sum_j \theta_j \cdot \phi_j(\vec x)$ using stepwise regression. One can use a greedy algorithm to solve it, e.g. ...
2
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0answers
15 views

Proving the given quadratic form is chi-squared $k$

Suppose $\underline{X}$ is an $m$-dimensional vector following multivariate Normal distribution i.e. $\underline{X}$~$N_m(\underline{\mu},\Sigma)$ where $\Sigma$ is positive definite. Let $B$ be a ...
1
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1answer
54 views

Compare linear models with and without an interaction effect

I want to compare the following two linear models: model 1: y = mean + A + B model 2: y = mean + A + A*B Is model 2 equivalent to y = mean + A + B + A*B? Can I ...
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0answers
38 views

Is the Naive Bayes family of classifiers linear?

There are a lot of places where you'll see the proof that Naive Bayes classifiers are linear, like this and this. But they always assume a special case of the family of Naive Bayes classifiers which ...
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0answers
24 views

Estimate of linear problem

I know that $xL(y) = m_x+K_{xy}K_y^{-1}(y-m_y)$. I have that the $E[x/y]=y^2$ and also $y\sim N(0,s^2)$. How can I calculate the linear estimator?
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1answer
88 views

Show that $E[\mu_i^2|X_i]=\sigma^2$ and $Var(\mu_i|X_i)=\sigma^2$

I'm a little stuck on this review problem so help would be greatly appreciated! Q: We have the regression model $Y_i=\beta_0+\beta_1X_i+\mu_i$ and we assume that the expected errors are $0$. We also ...
3
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1answer
80 views

How would you fit this model?

Section 2.1 of "Exegeses on linear models" (p. 3) describes a local linear model based on a second-order Taylor expansion. How would I go about fitting the model? I see that the first two terms ...
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1answer
99 views

Linear regression model mistakenly gives $R^2$ equal to 1

I'm using R to create a linear regression model from survey data about public sentiment for a new technology. I am encountering a problem where the addition of a new explanatory variable raises the ...
1
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1answer
26 views

Significance codes in linear model with factors

I am setting up a linear model in R and need help understanding the significance codes when one of my independent variables is a factor - i.e., dummy variable for each possible value For a scalar ...
3
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0answers
35 views

Prior for the coefficients of a linear regression model

I have a linear regression model $\bf Y=\bf{X}\bf{\beta}+\epsilon$. I want to assign a prior on $\bf\beta$ in order to derive the posterior predictive model $p(y_{predictive}|\bf{y},\bf{X},\beta)$. ...
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0answers
39 views

Is a model including a square root of a variable linear in the parameters? [duplicate]

Is the model $$ y = \gamma_0 + \gamma_1 + \sqrt x + \varepsilon $$ linear in parameters? ( $\varepsilon$ is the error term.)
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19 views

Linear regression with faster decrease in coefficient error/variance?

Suppose we have set of variables $Y$ and $X$, which know are related by a linear relation $y_i=\alpha x_i +\beta$, and important for us is to find $\alpha$ and $\beta$ and the error in estimating ...
3
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2answers
74 views

Is it an assumption of the normal linear model that explanatory variables are uncorrelated with the errors?

Some books seem to include an assumption for the normal linear model which I have never seen before. They say that there must be no correlation between between the explanatory variables and the ...
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0answers
26 views

How to do contrasts with weighted observations in R's linear model function lm()

As part of a simple simulation study, I have the following lines of code in R: ...
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0answers
6 views

Adjacent-period regression and time dummy

I have a sample of products' prices and their attributes across three brands to estimate price change. I have used linear adjacent-period regression with time dummies to capture average price change ...
2
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1answer
57 views

Endogeneity test instrumental variables

I'm reading a paper in which is used the following endogeneity test: First of all, we have the initial linear model: $$y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + e$$ $x_3$ is the ...
3
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1answer
46 views

Handling outliers in Bayesian linear regression

I am reading this post which talks about Robust Linear regression in a Bayesian setting. The particular blog post can be found here: http://twiecki.github.io/blog/2013/08/27/bayesian-glms-2/ There ...
0
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1answer
36 views

Why does adding more terms into a linear model always increase the r-squared value?

Many statistics textbooks state that adding more terms into a linear model always reduces the sum of squares and in turn increases the r-squared value. This has led to the use of the adjusted ...
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0answers
32 views

Interaction between continuous predictor and repeated-measures factor in R

How can I test for the presence of an interaction between a categorical repeated-measures factor and a continuous predictor? I'm using R. My data looks like this: ...
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2answers
61 views

How do I read this linear model output from R? [duplicate]

I normally use SPSS for my statistics, however after having some issues with violations I've had to try and run a linear model in R as apparently its more robust. Someone sent me the code that I ...
2
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0answers
27 views

Two univariate vs. multivariate analysis

Suppose I have 2 response variables $Y_1,Y_2$ and some predictor variables $x_j$. Is it the same if I use 2 separate linear models, one for each of the response variables, vs. using a multivariate ...
1
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1answer
53 views

Statistically significant difference in linear regression model predictions of the mean values

In my academic report I have a task to check whether or not mean values (for given two predictor values) predicted by the simple linear regression model are "statictically significantly different". I ...
4
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3answers
151 views

Transforming a variable when original variable does not have explantory power

Sometimes in multivariate linear regression, there will be one explanatory variable that does not contribute much in way of explanatory power. Then, we will perform a tranform on that variable, i.e ...
2
votes
1answer
64 views

Why take transpose of regressor variable in linear regression

I am stuck trying to understand the basic calculation of ordinary least squares. From wikipedia $$y = \beta X^T + \varepsilon$$ where $X$ is the independent variable, $Y$ is the dependent variable ...
2
votes
1answer
50 views

Sum of Square decomposition

Question about the Total, Explained, and Residual Sum of Squares. I am in the simple linear regression model. Could you help me clarify why the residual sum of squares (SSE where E stands for errors) ...
3
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1answer
67 views

Is it possible to seed RANSAC with a given line?

I am analyzing a stream of data and I want to seed every new instance with the best guess output (line) of the previous, so as to eventually converge. Given that Scikit Learn - RANSAC is an iterative ...
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0answers
43 views

Principal component regression on polynomial terms

One of the data sets I am working upon had 3 variables which were having almost 100% correlation among themselves. Since I am learning regression modelling I thought I'll do principal component ...
0
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0answers
26 views

Robust Standard Errors(SE) estimators vs SE estimators assuming Conditionally Homoskedasticity [duplicate]

If both the asymptotic Variance-Covariance matrix estimators (robust and non-robust) are consistent to the same matrix, i.e., both will have the same efficiency (True?), then what is the advantage of ...
5
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1answer
126 views

How to prove that Asymptotic Variance-Covariance matrix of OLS estimator is Positive Definite?

I'm trying to understand why the asymptotic Variance-Covariance($\text{Avar}(b)$) matrix of OLS estimator is Positive Definite(PD), like it's stated in Hayashi's book on page 113. We know that ...
2
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1answer
46 views

Can you add up effect sizes of two related variables (e.g. age + age$^2$) from a single regression model?

I am interested in the effect of age on outcome Y. I have two nested linear regression models to test linear and quadratic effects of age: Y= $\beta_0$ + $\beta_1$ some_covariate + $\beta_2$ Age + ...
1
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1answer
34 views

Confidence interval for a multiple of regression coefficient

I am trying to model relationship between length of stay of patients in hospital(Y) vs Age in years(X). The data set I've got doesn't specify the unit of length of stay. So now estimated value of my ...
0
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1answer
26 views

MSEP and R2pred for Linear Model

I have two set of data 1-Training (Calibrating) 2-Test. With these datasets, I Fit the model using first dataset. predict using the second dataset x-variables I have to test the closeness of the ...
1
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1answer
35 views

Rearrange regression equation that includes a dummy variable

This is my regression equation: $10 = 5.44 + 0.26X_1 - 3.19X_2$ $X_2$ is a dummy predictor with two levels. Assume that the value of $X_2$ is 1 therefore regression equation is: $10 = 5.44 + ...