Linked Questions
21 questions linked to/from Independent variable = Random variable?
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Why isn't X treated as a random variable in linear regression MLE? [duplicate]
I am very confused by this because when I watch videos or read about MLE with linear regression it seems to be commonly assumed that $X$ is fixed or that if it is random we don't care for the purposes ...
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What happens if we assume predictors are random variables in linear regression? [duplicate]
In linear regression or Gaussian-Markov framework,
$$Y = \beta_0 + \beta_1X+\epsilon, $$
where $\epsilon\sim(0,\sigma^2)$
we usually assume $X$ is non-random. In our statistics class, professors ...
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Question regarding "independent variables" term in regression analysis definition [duplicate]
Definition:
Regression analysis is used for explaining or modeling the relationship between a single variable Y, called
the response, output or dependent variable, and one or more predictor, input, ...
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What is the difference between variable and random variable?
I know that "variable" means "values which vary." In a simple linear regression model :
$$Y=\beta_0+\beta_1X+\epsilon$$
$X$ is variable that is the values of $X$ vary. Why is $X$ not a random ...
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2
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What justifies this calculation of the derivative of a matrix function?
In Andrew Ng's machine learning course, he uses this formula:
$\nabla_A tr(ABA^TC) = CAB + C^TAB^T$
and he does a quick proof which is shown below:
$\nabla_A tr(ABA^TC) \\
= \nabla_A tr(f(A)A^TC) \\...
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2
answers
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When are OLS linear regression parameters inaccurate?
Q1: Show quantitatively that OLS regression can be applied inconsistently for linear parameters estimation.
OLS in y returns a minimum error regression line for estimating y-values given a fixed x-...
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2
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Relationship between distribution fitting and simple regression?
This is a bit of a conceptual question that has been nagging me for a long time.
Based on a set of data, $(X_1, X_2, X_3, \ldots, X_k)$, with sample size $i = 1 \ldots n$ ,
is there an explicit ...
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3
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Normal Regression Model
Could someone please clarify the part highlighted in red?
Why the conditional density?
I am having hard time understanding why the statement is about conditional density
I don't understand why saying ...
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2
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Conditional expectation function
Consider the standard linear regression model given by
$Y = XB + \varepsilon$.
$E[Y\mid X] = XB$ if $E[\varepsilon \mid X] = 0$.
We say that the conditional expectation function is a random ...
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2
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Linear Regression Function Notation
Some books write linear regression function in the following way:
$$ Y = a + b \times X + u$$
While others write it in the following way:
$$ Y_i = a + b \times X_i + u_i$$
$ Y $, $ X $, $ Y_i $ ...
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1
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Synonyms of independent variable and origins of the names
The independent variable(IV) of a statistical model is a variable that is not dependent on the other variables in the model.
While I have been studying statistical modeling, I've kept embarrassed with ...
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1
answer
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Understanding the randomness of y in linear regression model
Suppose we have n data observations $\left\{y_i, \underline{x_i}\right\}_{i=1}^n$. We can concatenate the $x_i$ into $X$.
We have $y_i=h^TX + \epsilon_i$.
I understand that, since we have observed ...
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1
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Intuition on simple linear regression signal plus noise model
I'm currently studying linear regression on this book
"F.M. Dekking - A Modern Introduction to Probability and Statistics: Understanding Why and How" where the signal+noise model is presented:
$Y_i =...
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Does the 'no serial correlation' condition for regression only make sense with respect to a sample and not the population?
In this post, one of the answers provides the following information about the assumptions of linear regression in the case of random design (as opposed to fixed design):
The usual regression model is $...
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