Question

Which regression model best fits the data set?

(2,13),(4,8),(5,7.5),(7,7)


(1 point)
Responses

linear

linear

quadratic

quadratic

exponential growth

exponential growth

exponential decay

Answer 1

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.

1. **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.

2. **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.

3. **Exponential Growth**: This model would imply that the values increase quickly, which does not seem to fit the data.

4. **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**.