Pitch for Correlation Quiz

Hamish222
July 8, 2016

Motivation

Many students struggle to develop an intuition for the (Pearson) correlation coefficient.

The “Correlation Quiz” Shiny App presents random data of the form \[ (x_i, a_0 + a_1 x_i + \epsilon_i), \] where \( a_0 \) and \( a_1 \) are constants and \[ \epsilon_i \sim N(0, \sigma^2), \] and it gives the user the opportunity to guess the corresponding value of \( r \).

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This tends to be more difficult with few points and a correlation near zero, but the user can change the number of points with a slider.

Shiny Example

Here is an example from the Correlation Quiz Shiny App.

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Shiny Example (Continued)

Including the least-squares regression line indicates that \( r>0 \).

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Shiny Example (Continued again)

Students can reveal the value of \( r \) (\( r \approx 0.258 \) in this case) at the bottom when they are ready.

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