Okay, let's analyze the r^2 values for the 4 options:
a. y=16.5839•1.0185^x
r^2 is undefined, as this is an exponential model. We cannot determine how well it fits the data based only on r^2.
b. y=0.985515x-2.81333
This is a linear model, so r^2 would be between 0 and 1. Without knowing the actual r^2 value, we cannot determine how good the fit is.
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
This is a 3rd order polynomial model. Again, without the r^2 value, we cannot determine the quality of fit. It could be a good or poor fit.
d. y=0.00182197x^2+0.785098x+1.195
If this model has the highest r^2 value (closest to 1), it would indicate the best fit to the data of the options.
In summary, without seeing the actual r^2 values calculated from the data for each model, we cannot definitively say which option is the "best fit". The model with the r^2 closest to 1 would likely be the best, but r^2 only tells part of the story. Other factors like complexity, interpretability, and residual analysis also matter. But based solely on r^2, the quadratic model d seems the most likely to be the best fit, as long as its r^2 value is high.
Does this help explain the approach? Let me know if you have any other questions!