Does the second order polynomial in age that was estimated have a maximum or a m

Question

Does the second order polynomial in age that was estimated have a maximum or a minimum? At what value for AGE" does the polynomial have its maximum or minimum

Model 1: OLS, using observations 1-5190 Dependent variable: DVISITS coefficient std. error t-ratio p-value 0.0527643 0.184703 -0.0972459 -0.0461370 0.0735133 0.423229 0.473790 0.0331724 0.4729 0.6626 0.8374 0.1643 const AGE AGESO INCOME LEVYPLUS FREEP0OR -0.123635 HSCORE HOSPADMI MEDICINE 0.7178 0.4364 -0.2053 -1.391 0.000250658 0.0220170 0.01138 0.9909 0.0538149 0.00508769 0.0210130 13.98 0.00749805 13.26 0.0216 3.94e-18 1.28e-43 1.65e-39 -2.297 8.713 0.0443272 0.293756 0.0994519 Mean dependent var 0.301734 S.D. dependent var 0.798134 Sum squared resid 2882.143 S.E. of regression 0.745849 R-squared F (8, 5181) Log-likelihood Schwarz criterion 11752.82 Hannan-Quinn 0.128072 Adjusted R-squared 0.126726 4.0e-148 11693. 83 11714.46 95.12580 P-value(F) -5837.913 Akaike criterion Excluding the constant, p-value was highest for variable 5 (LEVYPLUS)

Explanation / Answer

y^ = c + 0.184703* age - 0.0972459 *age^2

this is inverted parabola, hence it has maximum

maxima occur when

dy^/d age =0

or 0.184703 -2* 0.0972459 *age = 0

age = 0.184703 /(2* 0.0972459)

= 0.94966985

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