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 \((2, 13)\), \((4, 8)\), \((5, 7.5)\), and \((7, 7)\), we need to consider the nature of the data points.

1. **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.

2. **Quadratic Regression** could possibly fit if there’s a parabolic trend. As the y-values decrease, it’s possible there’s curvature.

3. **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**