All Questions
11 questions
13
votes
3
answers
999
views
What does it mean for observations to be uncorrelated and have constant variance?
I am learning about linear regression from the textbook Elements of Statistical Learning by Friedman, Tibshirani, and Hastie. In this section they suppose we have a set of training data $(x_1, y_1), \...
- 343
1
vote
0
answers
17
views
How can I reduce correlation between two independents variable?
Edvard, the evaluator in sample B, does not know Richard, the target subject in sample A. However, the two, independently, give the same answer/Likert value (1-5) to 30% of the questionnaire items. It ...
- 11
4
votes
2
answers
521
views
Why do we use $R^2$ instead of $R$ in linear regression?
$R^2$ equals the "amount of variance explained by the model".
However, we rarely use variance in descriptive statistics. We say a sample's weight is 78 ± 13 kg, which is $\bar x$ ± $\sigma$ (...
- 51
0
votes
0
answers
28
views
Proving non-correlation with very disperse distributions
I'm fairly new to statistics and came up with a problem.
I have a sample with a variation coefficient CV = 0.517 for variable x, and I want to prove this variable is not correlated with a second ...
- 235
2
votes
1
answer
129
views
When using Linear Models with random covariates, is it the pearson correlation that determines the reduction of the residual variance?
Typically, if you have normally distributed dependent variable Y with variance $\sigma_Y^2$ a treatment indicator and a random covariate that is also normally distributed, then when fitting a linear ...
- 73
4
votes
2
answers
675
views
If two predictors are uncorrelated, is the variance explained by multiple regression the sum of variance explained by both linear regressions?
Pretty much what it says in the title. I don't know too much about statistics and I worry I'm getting this wrong.
There are variables $X$ and $Y$, they are uncorrelated by design, because one has ...
0
votes
0
answers
29
views
Can I determine what the correlation matrix is if I have regression coefficients and standard errors?
I am trying to reverse engineer a manuscript and was wondering if I can get a correlation matrix or the covariance-variance matrix from values reported in a paper. Can I use the reported regression ...
- 662
0
votes
1
answer
311
views
How to interpret these R regression coefficient results? [closed]
I'm really super new to R and am doing the most basic stuff for a beginner's statistics class. I've been staring at this question for a while and can't work out what I'm meant to do.
Here's the ...
- 1
3
votes
2
answers
452
views
Adjusted R-Squared in terms of variance
Say that I am performing a multiple linear regression with 3 variables. If I want to say that two of these variables account for some percentage of the observed variance in the third variable, should ...
5
votes
1
answer
701
views
correlation coefficient in linear regression
My interest is to develop a relation of the correlation coefficient when the data (both the dependent and independent variables) have measurement errors.
Intro
The measured values are related to the ...
- 460
25
votes
3
answers
14k
views
Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
I want to fully grasp the notion of $r^2$ describing the amount of variation between variables. Every web explanation is a bit mechanical and obtuse. I want to "get" the concept, not just mechanically ...
- 3,017