The question involves analyzing the Hammett plot for the given transformation. The Hammett equation is used to relate the reaction rates of a series of related compounds to the substituents present on the aromatic rings. It is represented as:

where \(k\) is the rate constant for a substituted compound, \(k_0\) is the rate constant for the unsubstituted compound, \(\sigma\) is the substituent constant specific for a given position, and \(\rho\) is the reaction constant.

For this transformation, we notice:

• The reaction involves the change of a phenolic compound.
• The substituents \(X\) affect the acidity and reactivity of the phenolic group.
• Typically, electron-withdrawing groups increase the acidity, impacting the reaction rate.

The Hammett plot, therefore, shows the effect of substituents on the reaction rate. The correct Hammett plot for this transformation indicates a direct correlation between \(\log \left(\frac{k}{k_0}\right)\) and the substituent constants \(\sigma\). As the data is linear, it supports the use of the Hammett equation.

The correct answer is the plot showing a positive correlation with a slope reflecting the electron-withdrawing nature of the substituents enhancing the reaction rate.