The Bigger the Stop Sign, the More Expensive It Is $\mathrm{R}$

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: sqrt(cost)
$\mathrm{R}$ (correlation coefficient) $=0.98946627$
$R-s q=0.97904349$
s: 0.2141

$\begin{array}{lrr}\text { Parameter } & \text { coeff } & \text { se } \\\text { Intercept } & 1.1857 & 0.4346 \\\text { height } & 0.1792 & 0.0151\end{array}$



-Do you think this transformation for linearity was successful? Why?