All Questions
15
questions
3
votes
1
answer
343
views
Why is the sum of individual Spearman's rho squared less than 1 as opposed to Pearson's r in a synthetic example?
A relatively low number of iid random vectors of a relatively high dimension (10,000) are added up together element wise:
$$\sum_{i=1}^{n}X_i=Y$$
where $dim(X_i)=dim(X_j)=dim(Y),\forall i,j$ and $dim(...
- 301
3
votes
1
answer
174
views
Strange definition of coefficient of determination
In Wei and Kusiak, 2015 a metric is used to evaluate the performance of a time-series prediction model. The paper calls it
[the] correlation coefficient ($R^{2}$)
and defines it as
$R^{2} = 1-\frac{...
- 135
6
votes
1
answer
448
views
Why normalize the vectors to calculate the Pearson correlation coefficient?
I learned from this answer that the correlation $R$ is $\cos(\theta)$ and $\theta$ is the angle between a dependent vector $Y$ and an independent vector $X$, but I learned from this article that the ...
- 6,810
1
vote
1
answer
87
views
Adjusted R2 Validity for Big amounts of observations
I am working with a dataset that has a big amount of observations (2000). The purpose of my work is to find which dependent variables (x1, x2, x3...) are linked to my independent variable (y). I have ...
- 13
0
votes
0
answers
13
views
Total inconsistence between Pearson correlation in a correlation matrix vs Pearson test AND Rsquare smaller than Pearson [duplicate]
I have a very urgent issue that I need to solve this weekend.
If I create a linear model between 2 variables and look for the R square with this code:
...
- 1
6
votes
1
answer
7k
views
Simple linear regression: R2 not equal to squared Pearson coefficient
The R2 of a simple linear regression model is the squared Pearson
correlation coefficient (r) between the observations and the fitted
values.
Isn't the above in contradiction with the fact that the ...
- 6,187
1
vote
2
answers
1k
views
How to construct (simulate) data that will have a given coefficient of determination?
I want to produce random sample bivariate data that will have a given coefficient of determination and a given linear regression model. In particular, I want to understand how it should be constructed,...
- 111
1
vote
0
answers
474
views
Pearson and R^2 Correlation between three variables
Get it from someone else but don't quite know how to answer.
If $\rho_{X,Z}=0.4$, $\rho_{Y,Z}=0.3$, what is the range of $\rho_{X,Y}$? Here $\rho$ is the Pearson correlation coefficient.
We run a ...
- 11
0
votes
0
answers
35
views
Formula for confidence intervals for corelation of samples from non-normal distributions
My question is similar to Formula for 95% confidence interval for $R^2$ (I indeed want to corelate predicted with true values to obtain $R^2$).
The problem is their distribution is not normal. I ...
- 363
2
votes
2
answers
7k
views
When is $R^2$ the same as Pearson's $r$ squared?
I am a bit confused about the relationship between Pearson's $r$ and the Coefficient of Determination $R^2$.
$$
r = \frac{\sum\limits_{i = 1}^n (x_i - \overline x)(y_i - \overline y)}{\sqrt{\sum\...
- 23
0
votes
0
answers
1k
views
What do r (Pearson correlation coefficient) and R^2 stand for? [duplicate]
As far as I understood, R squared explains how much the variation in Y is explained by its linear association with X. And it's used as an indicator for goodness of fit of a linear model.
Then when ...
- 133
5
votes
1
answer
3k
views
High Pearson correlation, but very low coefficient in multiple regression analysis?
I have been running a few linear regression models to test the absolute and relative effect of several independent variables related to spending/investment on different tools on one measure of ...
- 51
1
vote
1
answer
1k
views
Relation between $R^2$ and the covariate correlation matrix
I'm quite new to Statistics and I'm facing a problem.
Is there any relation between $R^2$ and the correlation matrix of the covariates?
A short example is (case with 2 covariates) :
A7 ~ A1 + A2
<...
- 403
0
votes
1
answer
109
views
Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum?
Why can't we add all the individual Pearson's $r$'s in a multiple regression and calculate $R^2$ based on this sum? Is there an easy mathematical explanation to this as $r^2$ is squared and don't add ...
5
votes
2
answers
13k
views
Estimate error of prediction from R-square
What I have:
a linear model $y=a_0+a_1x$ with given parameter estimates,
the number of values used for fitting the model,
the Pearson R² value.
I need to estimate errors of prediction. I don't see a ...
- 6,721