To determine which of the provided options could use both intercepts to produce viable solutions, we need to consider the nature of the relationships between the variables in each pair.
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Temperature, number of car rentals: This could have a viable relationship, especially in terms of seasonal effects on car rentals (higher rentals in warmer weather), but might not logically use both intercepts.
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Number of nominations, number of awards: While a relationship exists (more nominations could imply more awards), it doesn't inherently use intercepts in a practical sense.
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Age, weight: There is a potential relationship here (generally age and weight might have some correlation), but again, the direct application of intercepts doesn't lead to significant useful analysis.
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Years of experience, starting salary: This is a common relationship where more experience typically correlates with a higher starting salary. In financial modeling, the intercept would often represent the base salary without experience, making both intercepts relevant in a business context.
Based on these evaluations, the option (years of experience, starting salary) is the one that could use both intercepts to produce viable solutions.