To determine which of the given pairs of variables could use both intercepts to produce viable solutions, we need to analyze each option:
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(temperature, number of car rentals): This relationship could be modeled linearly, as temperature may impact the number of car rentals (e.g., more rentals in warmer weather). The intercepts in this scenario could represent situations where there are extreme temperatures (very low or high) with possibly little to no rentals, but this may not yield a meaningful interpretation for intercepts.
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(number of nominations, number of awards): This relationship is likely to be positive but may not necessarily fit a linear model where both intercepts are meaningful. The intercept would represent scenarios where there may be zero nominations and also zero awards, which is sensible but less helpful.
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(year of experience, starting salary): Typically, this relationship can be modeled to show that with more years of experience, starting salary tends to increase. The intercept can represent a starting salary based on zero experience, which is a meaningful and relevant scenario, allowing for viable solutions.
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(age, weight): While there can be interesting relationships between age and weight, it's less clear how both intercepts would yield viable solutions in a linear context. Age has practical limitations (e.g., there’s a biological limit on how low it can go meaningfully), while weight can vary widely. The interpretation of intercepts here can be convoluted.
Given this analysis, the best fit for a relationship where both intercepts could provide viable solutions is:
(year of experience, starting salary).
This option has the clearest linear relationship where both intercepts are relevant and provide meaningful insights.
1 answer