The quadratic and logarithmic models, y = β₀ + β₁x + β₂x² + ε and y = β₀ + β₁ ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit? A) The quadratic model. B) The logarithmic model. C) The models are not comparable. D) The provided information is not sufficient to make the conclusion.

Question

Quizplus · Accepted Answer

To determine which model provides a better fit, we can examine the R-squared value for each model. The R-squared value for the quadratic model is 0.825, while the R-squared value for the logarithmic model is 0.906. Since the R-squared value is closer to 1 for the logarithmic model, it suggests that this model provides a better fit for the data than the quadratic model. Therefore, the answer is B, the logarithmic model provides a better fit.

The Quadratic and Logarithmic Models, Y = β0 + β1x

The Quadratic and Logarithmic Models, Y = β₀ + β₁x