Quantitative models of music. Writing in Chance (Fall 2004), University of Konstanz (Germa...

Quantitative models of music. Writing in Chance (Fall 2004), University of Konstanz (Germany) statistics professor Jan Beran demonstrated that certain aspects of music can be described by quantitative models. For example, the information content of a musical composition (called entropy ) can be quantified by determining how many times a certain pitch occurs. In a sample of 147 famous compositions ranging from the 13th to the 20th century, Beran computed the Z12-note entropy ( y ) and plotted it against the year of birth ( x ) of the composer. The graph is reproduced here.

a. Do you observe a trend, especially since the year 1400?

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b. The least squares line for the data since 1400 is shown on the graph. Is the slope of the line positive or negative? What does this imply?

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c. Explain why the line shown is not the true line of means.