A Linear Regression model shows an R2 (adjusted) of 0.90 and a P-value of 0.002. A Quadratic Regression model of the same data shows an R2 (adjusted) of 0.92 and a P-value of 0.000. What can you…

Question

Options

• AA linear model would be better than a quadratic model.
• BA quadratic model would be better than a linear model.
• CAny non-linear model would fit the data well.
• DAny linear or non-linear model would fit the data well.
• ENeither a linear or non-linear model fits the data well.
• FThe Residuals would be expected to be large for either a linear or quadratic.

• A
  2% (1)
• B
  4% (2)
• D
  76% (37)
• E
  4% (2)
• F
  14% (7)

Explanation

Both models demonstrate strong fit: each has a high adjusted R² (0.90 and 0.92, respectively) - meaning both explain most of the variance in the data - and both have statistically significant p-values (0.002 and 0.000, both well below the 0.05 threshold), confirming neither result is due to chance. Since the adjusted R² already penalizes for adding extra parameters, a 0.92 vs 0.90 difference is negligible and doesn't make one model clearly superior - both simply fit well. A is wrong because the quadratic's adjusted R² is actually slightly higher, not lower. B is wrong because a 0.02 difference in adjusted R² is not meaningful enough to declare the quadratic definitively better. C is wrong because we can only draw conclusions about the models actually tested - not "any non-linear model." E and F are wrong because the high adjusted R² values on both models indicate good fit and relatively small residuals, not poor fit.

Memory tip: Think of adjusted R² and p-value as a two-key lock - if BOTH are favorable across multiple models (R² near 1, p < 0.05), then all those models fit the data well, and you shouldn't feel pressured to crown a "winner" from the options.

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