Question

Th R2 values of different regression are found for a scatterplot. Which of the following would be the best mathematical model to use for the data?

A. Power model for a power regression R2= 0.522

B. Linear model for a linear regression R2= 0.237

C. Exponential model for an exponential regression R2=0.712

D. Quadratic model for a quadratic regression R2=0.698

Answer 1

The correct option is C. Exponential model for an exponential regression R2=0.712.

Explanation:

R2 measures the average differences between the data and the model.

If R2 equal to 1 then model will perfectly match. So, 1 is the maximum possible value for R2.

If the model is not a good fit, R2 decreases (the value of R2 can never be 0).

Thus, the value of R2 is in the interval (0, 1], and the closer to 1 the better the model represent the data.

Now, consider the provided options.

Since, the exponential model for exponential regression R2=0.712 has the value closer to 1 among all the models.

Therefore, the correct option is C. Exponential model for an exponential regression R2=0.712.

Answer 2

The correct answer is choice C; Exponential model for an exponential regression R2=0.712

Explanation:

The coefficient of determination (R2) determines the predictive power of the model. The greater the value of R2, the better the model fits the data. It also serves as an indicator of the overall goodness of fit of the data to a particular model. Hence, the Exponential model for an exponential regression R2=0.712 is the best mathematical model.

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