To determine which regression model best fits the given data set \((2, 13)\), \((4, 8)\), \((5, 7.5)\), and \((7, 7)\), we need to consider the nature of the data points.
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Linear Regression would imply a straight line that fits the data, while looking at the points:
- (2, 13) is much higher than the others.
- The points decrease but not in a consistent linear manner.
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Quadratic Regression could possibly fit if there’s a parabolic trend. As the y-values decrease, it’s possible there’s curvature.
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Exponential Growth/Decay would typically imply a consistently increasing or decreasing trend, respectively, which isn't necessarily present here.
Based on the values:
- The y-values start at 13 and decrease, but not linearly.
- It suggests that a quadratic model might capture the downward trend better as it can accommodate a U-shape.
Given all this, it is very likely that a quadratic model would best fit the set. However, it's best confirmed with statistical fitting methods (like R-squared values) to see if it significantly outperforms the linear model.
Response: quadratic
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