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
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**
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**