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Covariance(X, Y)

Computes an estimate of the covariance or weighted covariance between two uncertain quantities «X» and «Y». The covariance is a measure of the amount of linear dependence. A covariance of 0 indicates that the two quantities appear to be independent (although if there is a non-linear relationship, this is not necessarily the case), a positive value indicates that they tend to increase together, while a negative correlation indicates that an increase in one quantity tends to be accompanied by a decrease in the other.

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is the covariance normalized by the standard deviations so that the result ranges from -1 to 1. The covariance is not limited to any particular range.

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function accepts a covariance matrix as a parameter when specifying a multi-variate distribution.

Full declaration:


If you have a data set containing two variables, A and B , where data points are indexed by J , the covariance of A and B is computed using

Here J is referred to as the running index .

If you have an array in which you want to find the covariance of two columns, then you will apply the subscript operator to extract each column. For example, the following computes the covariance between historical revenue in 2002 and 2003 (where data points are indexed by J ).

Unweighted covariance treats all data or sample points as equally weighted. Weighted covariance computes the covariance when each data point may have a different weight. The optional «w» parameter may be used to specify a weight, which should be indexed by the running index (or by Leather Statement Clutch Harietta the Hare by VIDA VIDA Cheap Best Prices Cheap Sale Low Price Fee Shipping Amazon Footaction Very Cheap Cheap Online sEgXT5DH
if no running index is specified). For example, the following specifies an importance weight:

The global sample weighting, specified by the system variable SampleWeighting , is used by default.

Suppose each sample point is a vector along index I . A covariance matrix is a 2-D square symmetric matrix where each element (m, n) indicates the covariance of column I = m and column I = n . To compute a sample covariance matrix for a given set of data, create a second index, I2 as a copy of I :

With this index, the covariance matrix, index by I and I2 , is computed from data X using:

Or if data points are listed along an index other than Run , say J , this would be:

Copyright © 1969 and 1987 by Eric Carle Butterfly from The Very Hungry Caterpillar
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The Eric Carle Museumof Picture Book Art

Visit the carle

These onsite or outreach programs are designed to engage students with materials in ways that spark the imagination and inspire critical and creative thinking. Grounded in the Museum’s commitment to education through the arts, they also support the National and Massachusetts Arts Curriculum Frameworks for art education. To learn more about our educational approach at The Carle, see Our Approach . For more program options, see our Book-Centered Programs .

Art-Centered Programs include materials and are designed for between 8 and 25 participants. After reading the information below regarding program options and fees, please complete our online logo clutch White Moschino Buy Cheap Pre Order 38Op5QLL
with your selection.

Thinking with Found Materials - Ages 3 and up

This hands-on program encourages imagination, collaboration, and critical thinking. Presented with a thoughtful selection of "everyday stuff," students will be encouraged to reuse and reinvent found objects.

Bookmaking Basics - Ages 5 and up

The Studio’s approach to bookmaking centers on the idea that books can be a vehicle for imagining creative and innovative ways to communicate ideas. In this multi-sensory program, students will learn fundamental bookmaking vocabulary and techniques, focusing on one or two artist book structures per session. Arrays of interesting materials are provided to adapt the structure to best fit their ideas.

I Am an Artist - Ages 5 and up

This program engages participants in thinking about what it means to be an artist. Using Eric Carle's work as inspiration, the group will explore process, materials, and the often-asked question, "Where do ideas come from?" An optional multiple-visit program allows for a deeper exploration of Eric Carle's process and more time for students to explore their own ideas.

Possibilities in Print - Ages 9 and up

Picture books are collections of prints, or reproductions of original artworks, bound in sequential form. In this hands-on program, students will learn how picture books are produced, experiment with the tools and techniques of printmaking, and imagine, reproduce and share their own stories and ideas. Multiple-session bookings provide the opportunity to explore multiple printmaking methods.

Program Fees

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Accommodations / Per Diem

Any site beyond a four-hour roundtrip from the Museum will be asked to provide overnight accommodations for the outreach educator at his or her discretion. A per diem rate of $45 may also be applied to cover meals and incidental expenses incurred by the consultant/presenter.

The mission ofThe Eric Carle Museumof Picture Book Art,a non-profit organizationin Amherst, MA, is to inspire a love of art and readingthrough picture books.

The Eric Carle Museum of Picture Book Art


  • 600 West Walnut Street, Danville, KY 40422
  • 1.859.238.5200
EMERGENCY? Call HELP (ext. 4357) on the campus telephone system or 859.236.4357 from all other telephones.


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