The Bigger the Stop Sign, the More Expensive It Is $\operatorname{sqrt}(\cos t)$

question 144

Essay

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars.

To achieve linearity, the data was transformed using a square root function of cost. Here are the results and a residual plot.
Dependent Variable: $\operatorname{sqrt}(\cos t)$
$R$ (correlation coefficient) $=0.98946627$
$R-s q=0.97904349$
s: 0.2141
$\begin{array}{lrr}\text { Parameter } & \text { coeff } & \text { se } \\ \text { Intercept } & 1.1857 & 0.4346 \\ \text { height } & 0.1792 & 0.0151\end{array}$



-Interpret R-sq in the context of this problem.

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Definitions:

Herfindahl Index

A measure of market concentration and competition, calculated as the sum of the squares of the market shares of all firms within an industry.

Clayton Act

A U.S. antitrust law enacted in 1914 aimed at promoting fair competition and preventing monopolies.

Herfindahl Index

A measure of the size of firms in relation to the industry and an indicator of the amount of competition among them.

Horizontal Merger

A merger between firms that are in the same industry, often aimed at reducing competition and achieving economies of scale.