# Questions tagged [ellipse]

For on-topic questions involving the geometrical object ellipse, for example confidence ellipsoids. For purely mathemathical questions about ellipses, it is better to ask at math SE https://math.stackexchange.com/

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### Bivariate normal probability of being inside ellipse

Assume that $\mathbf{X}$ is a bivariate normal random variable \mathbf{\mu} = E\mathbf{X} = \begin{bmatrix} 0 \\ 2 \end{bmatrix} \ \text{and} \ \Sigma = Cov \ \mathbf{X} = \begin{bmatrix} 3 & 1 ...
46 views

### Why does running PCA on data representing a 2-D ellipse return the same ellipse with nonzero rotation?

I am trying to better understand PCA. I am aware that PCA can be used to reduce a problem from $n+1$ dimensions to $n$ dimensions. As I understand it (with a lot of help from this post), PCA is used ...
21 views

### Confidence interval of amplitude and horizontal shift

I have a linear model with sine and cosine wave as predictor. Y~$\alpha$sine(...)+$\beta$cosine(...). From the parameter estimation, I know the estimation of the coefficients are: $\hat\alpha$ = 0.65(...
43 views

### scatterplot in 3d

I have several points in $\mathbb{R}^{3}$. When I create a 3D scatterplot of the points, they seem to lie on an ellipsoid as shown in the above plot. How do I interpret the plot ? Does it indicate ...
4k views

### Proper way of estimating the covariance error ellipse in 2D

I am aware of this question but my issue is about two competing ways of obtaining the 2D covariance error ellipse in two competing answers over at StackOverflow. The first answer obtains the width ...
660 views

### Why is a confidence ellipse based on multivariate-t tighter than one base on multivariate norm (R)

I want to draw a 95% confidence ellipse around my bivariate data. Using ggplot2::stat_ellipse() with type="t" (for a bivariate-t ...
45 views

### Question about eigenvalues and ellipses

Please consider the snippet below out of Bishop's book on PRML. According to my understanding of an ellipse, the radii are $\sqrt\lambda_{1}$ along the horizontal axis ($w_1$) and $\sqrt\lambda_{2}$ ...
421 views

### Using ellipses, how can I visually compare two estimated covariance matrices in the presence of sampling uncertainty?

I have with me two data matrices each of dimension n x p where n is the number of rows of observations and p = 2 is the number of variables. Each data matrix yields a covariance matrix using the ...
161 views

### What is the correct name for a so-called “confidence ellipse”?

We often see the terminology "confidence ellipse". This is not correct: in dimension 2, an ellipse is a curve, and the confidence region is the interior of this curve, not the curve. Similarly, in ...
641 views

### How to estimate an ellipse's parameters from the points scattered around it? [duplicate]

The scatter plot shows two data series (x,y) the are placed somehow around a tilted ellipse. This is in fact the way I have drawn this example plot. Which statistics of the data sets are the most ...
548 views

### Determine whether the point is within PCA probability ellipse

Im following this example, up to a point where the guy visualises the PCA using biplot function. Just before that he uses ggplot to plot PCA results (PC1 x PC2) and adds, for each category, ...
1k views

### Ellipse formula from points

Question: Best way to derive an ellipse formula when given bunch of points (say 60 points which when connected draws an ellipse)? Background: Using R Momocs library function conf_ell which returns ...
425 views

### How to Draw an Ellipse around a Specific Portion of a Probability Density Function

I currently have a 2D probability density function and need to draw a 2D ellipse that circumscribes 50% of the probability "mass" (if that is the right terminology). I see lots of articles on how to ...
289 views

### Confidence ellipse formula (R) [duplicate]

What I have: A scatter chart(plot) of PCA. Plotted in JS. I have Rtools that Ive used to push PCA data to the client side. Assumption : The author in this post draws confidence ellipses around the ...
132 views

### Why should i remove zero when handling data?

I am trying to find out whether two variables X,Y are distributed as bivariate normal. Here is my procedure: check whether X is normal check whether Y is normal check whether scatter plot is follow a ...
163 views

### Select ellipsoid data cloud “equivalent” to a spherical data cloud

What will be your considerations when you've got to realize the intuitively plain, but meditatively manifold idea to create a data cloud which "the same as" that data cloud, only that it is not ...
16k views

### Real meaning of confidence ellipse

Reading about the true meaning of 95% confidence ellipse, I tend to come across 2 explanations : The ellipse that contains 95% of the data Not the above, but the ellipse that explains the variance ...