To determine which of the options could use both intercepts to produce viable solutions, we need to understand the context of each pair of variables and how they relate to one another.
a. (years of experience, starting salary): This relationship is likely to yield a positive correlation, meaning as years of experience increase, starting salary may also increase. The intercept here (when years of experience = 0) may not be feasible in a real-world sense, as it would imply a salary without experience, which may not be practical.
b. (number of nominations, number of awards): This could represent a positive relationship where more nominations lead to more awards. Both intercepts (zero nominations and zero awards) may have viable meanings, specifically that if there are zero nominations, then it is expected that the number of awards would also be zero.
c. (temperature, number of car rentals): This relationship could have a varying correlation depending on climate and season (higher temperatures might lead to more rentals in vacation spots). The intercepts here could be more abstract, but they may not produce meaningful real-world solutions at zero temperature or zero rentals.
d. (age, weight): There is typically a correlation here, but it is non-linear, as weight does not continuously change with age in a predictable manner. The intercepts might not yield practical meaning, especially with age being zero, which isn't a typical point of reference for weight.
Considering the above assessments, option b. (number of nominations, number of awards) is the best answer. Both intercepts here essentially provide a clear and practical interpretation regarding the relationships between the variables, confirming that a zero nomination implies zero awards, thus producing viable solutions.