Answer:
The model that best fits the data is the one with the highest value of [tex]R ^ 2[/tex]. In this case it is the quadratic, with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex].
Step-by-step explanation:
To find the different regression models, the Excel software was used.
For the linear regression model, the following equation was obtained:
[tex]y = 2.0809x + 1.291
[/tex]
with a coefficient of determination [tex]R ^ 2 = 0.8911
[/tex]
For the quadratic regression model, the following equation was obtained:
[tex]y = 0.1663x ^ 2-0.0498x + 4.8229[/tex]
with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex]
Finally, for the exponential regression model, the following equation was obtained:
[tex]y = 4.4281e ^ {0.1513x}[/tex]
with a coefficient of determination [tex]R ^ 2 = 0.9635
[/tex]
The coefficient of determination [tex]R ^ 2[/tex] measures how well a predictive mathematical model fits reality. The value of [tex]R ^ 2[/tex] is always between 0 and 1. The closer you get to 1, the more accurate is the built model.
Therefore, the model that best fits the data is the one with the highest value of [tex]R ^ 2[/tex]. In this case it is the quadratic, with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex]
The results obtained are summarized in the attached table.
