Linked Questions

1 vote
0 answers

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 ...
Tan's user avatar
  • 1,469
0 votes
0 answers

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 ...
AdmiralMunson's user avatar
0 votes
0 answers

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, ...
claudius's user avatar
  • 235
106 votes
10 answers

What is meant by a "random variable"?

What do they mean when they say "random variable"?
Baltimark's user avatar
  • 2,218
11 votes
3 answers

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 ...
ABC's user avatar
  • 1,685
16 votes
2 answers

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) \\...
MoneyBall's user avatar
  • 897
2 votes
2 answers

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-...
Carl's user avatar
  • 12.6k
2 votes
2 answers

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 ...
Coolio2654's user avatar
5 votes
3 answers

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 ...
gioxc88's user avatar
  • 1,180
4 votes
2 answers

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 ...
Snoopy's user avatar
  • 513
0 votes
2 answers

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 $ ...
G.T.'s user avatar
  • 146
3 votes
1 answer

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 ...
2 votes
1 answer

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 ...
learning's user avatar
  • 475
2 votes
1 answer

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 =...
Luca 's user avatar
  • 23
3 votes
0 answers

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 $...
ManUtdBloke's user avatar

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