Question

Compare the following models based on goodness of fit:

Model A: y=α₁+α₂ ln₂x₂+₃u RA²=0.75 Adjusted- RA²=0.74
Model B: In y=β₁+β₂x+β₃x+v RB²=0.74 Adjusted- RB²=0.73
Model C: lny=δ₁+ δ₂x₂+δ₃x₃+δ₄ lnx1+e RC =²0.78 Adjusted-RC² =0.72
Model D: y=y₁+y₄x₄+w RD²=0.76 Adjusted- RD² =0.75
a. B>C \& D>A; and other combinations cannot be compared
b. C>B \& D>A; and other combinations cannot be compared
c. C>D>A>B d
. D>A>B>C

Answer 1

Based on the adjusted R-squared values, Model D has the highest goodness of fit, followed by Model A, Model B, and Model C, in that order.

Step-by-step explanation:

When comparing the four models based on the goodness of fit, we should primarily consider the values for R-squared (R²) and adjusted R-squared. These values indicate how well the model explains the variation in the dependent variable. A higher R² indicates a better fit to the data. However, the adjusted R-squared is also important because it adjusts for the number of predictors in the model and prevents overestimating the goodness of fit for models with more variables.

Based on the given data:

• 
  
• Model A: Adjusted R² = 0.74
• 
  
• Model B: Adjusted R² = 0.73
• 
  
• Model C: Adjusted R² = 0.72
• 
  
• Model D: Adjusted R² = 0.75

Comparing these values:

1. 
   
3. Model D has the highest adjusted R², indicating the best goodness of fit.
4. 
   
6. Model A has the second highest adjusted R² value.
7. 
   
9. Model B is slightly lower than Model A in terms of good fit.
10. 
    
12. Model C has the lowest adjusted R², which denotes it as the least fit among the four.

Thus, the correct answer appears to be: D>A>B>C, with Model D having the best goodness of fit and Model C having the least.