The length (in mm) and age (in years) of a sample of 70 sunfish from a particular lake were recorded. A polynomial regression function of degree 5 was fit to the data using length as the response and age as the predictor. But the researchers are interested in whether a lower degree polynomial would be sufficient to describe the data. Some output is below.

> fit=with(df, 1m(Length~Age+I(Age/2)+I (Age^3)+I (Age/4)+I (Age^5))) > summary (fit) Call: 1m(formula = Length ~ Age + I(Age^2) + I(Age^3) + I(Age/4) + I (Age15) ) Residuals: Min 1Q Median 30 Max -19.192 -4.811 -1.241 4. 884 25 . 676 Coefficients: Estimate Std. Error t value pr(>|t|) (Intercept) 18 . 39883 94 . 48400 0. 195 0. 846 Age 65 . 11044 196. 87257 0. 331 0. 742 I (Age12) -10 . 09705 143 . 95373 -0. 070 0. 944 I (Age13) 2. 20121 47 . 60042 0 . 046 0. 963 I (Age14) -0. 50786 7. 26678 -0. 070 0. 945 I (Age15) 0. 03861 0. 41572 0. 093 0. 926 Residual standard error: 10. 36 on 64 degrees of freedom Multiple R-squared: 0.9148, Adjusted R-squared: 0. 9081 F-statistic: 137.4 on 5 and 64 DF, p-value: anova (fit) Analysis of Variance Table Response: Length of Sum Sq Mean Sq F value Pr (>F) Age 1 54213 54213 505 . 4191 anova (fit) Analysis of Variance Table Response: Length of Sum Sq Mean Sq F value Pr (>F) Age 1 54213 54213 505. 4191