Question

The 𝑅² values of different regressions 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

To determine the best mathematical model to use for the data, we should look at the \( R^2 \) values of the different regressions. The \( R^2 \) value indicates the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. A higher \( R^2 \) value suggests a better fit of the model to the data.

Here are the \( R^2 \) values for the models provided:

A) Power model: \( R^2 = 0.522 \)

B) Linear model: \( R^2 = 0.237 \)

C) Exponential model: \( R^2 = 0.712 \)

D) Quadratic model: \( R^2 = 0.698 \)

Among these options, the exponential model (C), with an \( R^2 \) value of 0.712, has the highest \( R^2 \) value. This indicates that it explains the most variance in the data compared to the other models listed.

Therefore, the best mathematical model to use for the data is:

**C) Exponential model for an exponential regression \( R^2 = 0.712 \)**.