To determine which of the options could use both intercepts to produce viable solutions, we need to consider the relationship between the variables in each pair. Here’s a breakdown of each option:
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(years of experience, starting salary): This relationship typically implies that higher years of experience would correlate with higher starting salaries, where the intercept could represent starting salary with zero years of experience. This is a viable option.
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(number of nominations, number of awards): This option suggests a relationship where more nominations could lead to more awards, but it might not always be linear or proportional. The intercepts may not provide useful insights in this case, as having zero nominations may not necessarily yield zero awards in all contexts.
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(age, weight): This relationship may not inherently have a linear connection or meaningful intercepts. The variables can vary widely and do not have a clear connection where intercepts would yield viable solutions.
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(temperature, number of car rentals): Although there could be a relationship suggesting that higher temperatures could lead to more car rentals (especially in tourism), the use of both intercepts is less straightforward and context-dependent. For example, a temperature might not logically correlate directly with the number of car rentals in a linear manner.
Based on this analysis, the most viable option that could use both intercepts to produce meaningful solutions is:
(years of experience, starting salary).