Linked Questions

0
votes
0answers
25 views

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, ...
89
votes
9answers
17k views

What is meant by a "random variable"?

What do they mean when they say "random variable"?
9
votes
3answers
15k views

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 ...
11
votes
1answer
680 views

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) \\...
2
votes
2answers
1k views

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-...
4
votes
3answers
842 views

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 ...
1
vote
2answers
729 views

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 ...
2
votes
1answer
904 views

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 ...
4
votes
2answers
414 views

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 ...
0
votes
2answers
858 views

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 $ ...
2
votes
1answer
304 views

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
1answer
274 views

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 =...
0
votes
1answer
191 views

Distribution of simple linear model

Question: Am I correct in assuming that the below statement only makes sense if we're conditioning on realised data? I'm finding it hard to understand the following statement; For a simple normal ...
1
vote
2answers
80 views

What is the stastical perspective of regression? [duplicate]

When you giving a data set as a table. The rows are the observation (e.g. measurement of different humans) and columns are your features (height, weight, ...) and one column is the one you want to ...
3
votes
0answers
98 views

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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