To determine the best-fitting model for the scatterplot of basketball card values over time, we need to consider the general shape and trend of the data points. Here's how you can decide based on typical characteristics of the models discussed:
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Linear model: This would imply a constant rate of increase or decrease in value over time. If the points form a straight line, or if you see a steady linear increase, this could be a good fit.
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Exponential model: This is suitable if the values increase quickly over time, indicating that each subsequent year corresponds to a percentage increase rather than a fixed amount. Data that curves upward steeply might suggest an exponential growth pattern.
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Quadratic model: This would suggest that the values increase or decrease at varying rates, perhaps starting slowly and then accelerating — or vice versa. The data would have a parabolic shape.
Without seeing the actual scatterplot, the choice of the model largely depends on the overall pattern of the plotted points.
- If the points display an ascending curve that grows faster over time, an exponential model may be best.
- If they suggest a straight-line relationship, a linear model might fit.
- Conversely, if they curve in a parabolic fashion, a quadratic model might be appropriate.
You may need to analyze the scatterplot to look for these characteristics to select the appropriate model. If I had to guess based on the options given, for values of basketball cards, an exponential model might often be appropriate due to the nature of collectibles typically appreciating in value over time at increasing rates.
However, please analyze the scatterplot visually to make a more informed decision.
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