Research Statistics Central

 Problem:   You are running a standard quadratic (polynomial) regression analysis, and are specifically interested in the X and Y values at the peak.  If you use standard regression software, typically there will be no option that allows the peak to be estimated, with standard errors. Example:   You are studying Growth as a function of Age.  Of particular interest is when maximum Growth occurs, and at what Age. SAS code to generate artificial data, and run the analysis is: data one; do Age=1 to 20; Growth=95 + 2.7*Age - .3*Age*Age + 5*rannor(22); end; proc nlin plots=fit; parms int=2 lin=1 quad=1; model Growth = int + lin*Age + quad*Age*Age; estimate 'Age at peak' -lin/(2*quad); estimate 'Growth at peak' int + lin*(-lin/(2*quad)) + quad*(-lin/(2*quad))*(-lin/(2*quad)); run; The standard quadratic regression model with intercept, linear and quadratic slopes, is coded into Proc NLIN which has the ability to estimate any function of the parameters.  The peak est