Which regression model best fits the data set? (2, 13); (4, 8); (5, 7.5); (7, 9) , (8, 12) (1 point) linear quadratic exponential growth exponential decay

Answer 1

To determine which regression model best fits the provided data set, we can examine the nature of the data points:

1. Data Points:

   • (2, 13)
   • (4, 8)
   • (5, 7.5)
   • (7, 9)
   • (8, 12)

2. Visualizing the Data: It can be helpful to plot the points on a scatter plot to see if they follow a linear trend, a quadratic curve, or exponential growth/decay.

3. Analyzing the Trend:

   • Linear: If the points show a straight-line trend, a linear regression would fit well.
   • Quadratic: If the pattern seems to curve upwards or downwards significantly, a quadratic model could be considered.
   • Exponential Growth/Decay: If the data points appear to increase or decrease rapidly in a non-linear fashion, exponential functions may fit.

4. Initial Observations:

   • The y-values start high at x = 2 (13) but decrease to 7.5 (at x = 5), then rise again to 12 (at x = 8). This suggests some non-linear behavior, but it does not display a classic exponential growth or decay.

Based on this qualitative analysis, the data points appear to first decrease and then increase, which could suggest a possible quadratic fit.

Conclusion

While without actual calculations or a software fit we cannot definitively state which model is the best fit, based on the general trend observed, it is likely that a quadratic model would be the most suitable fit for this data set.

However, for precise fitting, one would typically use regression analysis software or calculations to ascertain which model minimizes the error for the given data points.