To determine which regression model best fits the given data set \((2,13), (4,8), (5,7.5), (7,7)\), we need to consider the pattern of the data points.
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Linear Regression: A linear model would suggest a constant rate of change. The points show a distinct downward trend, which could suggest that a linear model might fit.
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Quadratic Regression: This model would allow for a curve. If the data initially increases or decreases at a rate that changes, a quadratic model might be suitable.
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Exponential Growth: This model would imply that the values increase quickly, which does not seem to fit the data.
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Exponential Decay: This would imply a rapid decrease which levels off, which also does not appear to describe the trend in the given data.
With the information provided, and visualizing the points:
- \(y\) values decrease as \(x\) increases but not at a constant rate, suggesting a potential curve, but not quite as an exponential function.
Considering the data points, they seem to fit more closely with a quadratic model due to the decreasing nature that isn't consistent with a constant slope.
Therefore, the best fitting model for the data set is quadratic.