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Converting Quarterly Data into Monthly Using Cubic Spline Interpolation

(Be sure to see this post and related discussion thread at Chamberlain Economics, L.L.C.)

A common problem with time-series data is getting them into the right time interval. Some data are daily or weekly, while others are in monthly, quarterly …

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A More Elegant View of the Correlation Coefficient

One of the first things students learn in statistics is the “correlation coefficient” r, which measures the strength of the relationship between two variables. The formula given in most textbooks is something like the following:

where x and …

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A Simple Way of Solving Exact Ordinary Differential Equations

Exact differential equations are interesting and easy to solve. But you wouldn’t know it from the way they’re taught in most textbooks. Many authors stumble through pages of algebra trying to explain the method, leaving students baffled.

Thankfully, there’s an …

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The Linear Algebra View of Calculus: Taking a Derivative with a Matrix

Most people think of linear algebra as a tool for solving systems of linear equations. While it definitely helps with that, the theory of linear algebra goes much deeper, providing powerful insights into many other areas of math.

In this …

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A Simpler Proof of the Bolzano-Weierstrass Theorem

A while back I posted a long proof of the Bolzano-Weierstrass theorem — also known as the “sequential compactness theorem” — which basically says every sequence that’s bounded has a subsequence within it that converges. Here’s a much shorter and …

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An Easy Derivation of the Volume of Spheres Formula

Working 2,000 years before the development of calculus, the Greek mathematician Archimedes worked out a simple formula for the volume of a sphere:

Of his many mathematical contributions, Archimedes was most proud of this result, even going so far as …

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