Question at position 20 You fit a polynomial regression model using Diastolic Blood Pressure regressed on Age. To find the best polynomial model, you tried polynomial with degree from 2 to 5. Based on the R output below, which of the following statements is correct? . The best model is polynomial with degree 5 because it has the highest R-square and lowest residual standard error. Without further information, no conclusion can be made about which model is the best. The best model is polynomial with degree 2 because it has the largest F statistic thus the smallest p-value for overall model significance. The best model is polynomial with degree 4 because the polynomial with degree 5 has a non-significant term for degree 5. None of them is correct!Clear my selection

Question

Question at position 20 You fit a polynomial regression model using Diastolic Blood Pressure regressed on Age. To find the best polynomial model, you tried polynomial with degree from 2 to 5. Based on the R output below, which of the following statements is correct? .  The best model is polynomial with degree 5 because it has the highest R-square and lowest residual standard error. Without further information, no conclusion can be made about which model is the best. The best model is polynomial with degree 2 because it has the largest F statistic thus the smallest p-value for overall model significance. The best model is polynomial with degree 4 because the polynomial with degree 5 has a non-significant term for degree 5. None of them is correct!Clear my selection

BlackTom AI · Accepted Answer

Let me walk through each option and weigh what the R output tells us about model adequacy across polynomial degrees.
Option 1: The best model is polynomial with degree 5 because it has the highest R-square and lowest residual standard error.
In the output, while the degree-5 model does show a very small residual standard error and a sizable R-squared, those metrics alone can be misleading for model selection when higher-degree terms may be non-significant or cause overfitting. The presence of a non-significant term among the degree-5 coefficients would argue against simply picking degree 5 based on R-squared alone, because R-squared tends to increase (or at least not decrease) with model complexity even if the added terms do not meaningfully improve the fit. Therefore, this criterion (highest R-squared and lowest residual SE) is not sufficient by itself to claim degree 5 is best, especially if terms are not significant.
Option 2: Without further information, no conclusion can be made about which model is the best.
The output includes detailed coefficient tables, standard errors, t-values, and p-values for each polynomial degree (2 through 5), along with residual standard error and F-statistics. While one should be cautious, the presence of significant F-tests and per-term significance across degrees provides information. Saying “no conclusion” ignores the available evidence about term significance (particularly the non-significant degree-5 term). Hence this statement is overly conservative given the displayed results.
Option 3: The best model is polynomial with degree 2 because it has the largest F statistic thus the smallest p-value for overall model significance.
From the R output, the degree-2 model has an F-statistic of 251.7 with p-value extremely small, but we should compare with degree-3, degree-4, and degree-5 models. The degree-3 model has a larger F-statistic (169.4) and a highly significant overall p-value, but the degree-4 and degree-5 models show even larger F-statistics and still highly significant p-values. The observation that degree-2 has the largest F-statistic among all is false — degree-4 and degree-5 show larger F-statistics and thus stronger overall model significance. Therefore this statement misidentifies which degree maximizes the overall model significance.
Option 4: The best model is polynomial with degree 4 because the polynomial with degree 5 has a non-significant term for degree 5.
This matches the pattern in the output: the degree-5 model includes a term poly(Age, degree = 5)5 with a t-value around -1.43 and p-value about 0.153, which is non-significant at conventional levels. The degree-4 model has all its terms significant (or at least the degree-4 terms show strong significance) and an F-test with a very small p-value (< 2.2e-16) and a substantial R-squared. The non-significance of the extra degree-5 term suggests that the additional complexity of degree 5 does not meaningfully improve the model and may be overfitting, so stopping at degree 4 is reasonable. This aligns with standard model-diagnostic reasoning where a non-significant higher-degree term argues for a simpler model.
Option 5: None of them is correct!
Given the presence of a non-significant degree-5 term and the improved parsimony and maintained significance with degree 4, this option would be incorrect because there is a justifiable best model among the presented choices, namely the degree-4 model for the reasons described in option 4.

In summary, evaluating the progression from degree 2 to degree 5 shows that while higher degrees can inflate fit metrics, a non-significant term in the highest-degree model (degree 5) indicates that the extra complexity is not warranted. The degree-4 model provides a good balance of explanatory power and parsimony, and the evidence from the output supports selecting degree 4 over degree 5. The other options either rely on incomplete criteria, misinterpret the direction of model significance, or ignore the non-significant term issue in the degree-5 model.

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