Final answer:
The variable that is likely to be linked to both shoe size and reading score is the student's age, as it corresponds to physical growth and educational progression.
Step-by-step explanation:
The variable likely linked to both shoe size and reading score could be the age of the student. As children grow older, their shoe sizes tend to increase, which is simply due to their physical growth over time. Similarly, the reading score is likely to improve as the student gets older because of the additional years of education and practice in reading. Thus, we can understand this positive correlation by considering the effect of the student's age on both variables.
Considering other options, the state in which the student lives is less likely to be directly linked to both variables in a predictable way. The height of the student's parents might influence the student's eventual shoe size, but not directly their reading score. The student's eye color is not related to shoe size or literacy skills, showing no causal or dependent link between these variables.