Question

A scatterplot containing several values is found to have a linear regression 𝑅² value of 0.883, a quadratic regression 𝑅² value of 0.537, an exponential regression 𝑅² value of 0.492, and a logarithmic regression 𝑅² value of 0.912. Which mathematical model best fits the scatterplot?

A) linear model
B) quadratic model
C) exponential model
D) logarithmic model

Answers

GPT-4o mini
To determine which mathematical model best fits the scatterplot, we can compare the \( R^2 \) values of the different models provided. The \( R^2 \) value indicates how well the model explains the variability of the data, with a value closer to 1 indicating a better fit.

The given \( R^2 \) values are:
- Linear regression: \( R^2 = 0.883 \)
- Quadratic regression: \( R^2 = 0.537 \)
- Exponential regression: \( R^2 = 0.492 \)
- Logarithmic regression: \( R^2 = 0.912 \)

Among these, the logarithmic regression has the highest \( R^2 \) value of 0.912, indicating it explains a greater amount of the variability in the data compared to the other models.

Therefore, the mathematical model that best fits the scatterplot is:

**D) logarithmic model**

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