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A study was performed in which 72 children were measured in order to examine how the weight to height ratio changes as kids get older. The ratio and age (in months) were recorded for each young participant.

Fit a quadratic curve to the sample data to model the relationship between weight to height ratio and age, and give its equation. Display this curve on a scatterplot of the data. For your model, Ratio will be the response variable and Age will be the explanatory variable.

Lee Creighton
SAS Institute Inc.

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The Growth data set is the recordings of the weight to height ratios and ages (in months) of 72 children.

These are the variables in the data set:

Sall, J., Creighton, L., & Lehman, A. (2006). JMP Start Statistics, Third Edition. Cary, NC: SAS Institute Inc.

Using SAS Enterprise Guide, the estimated quadratic fit to the data is given by the equation
predicted ratio = 0.6022 + 0.01060age – 0.00007337age^2.

To create the scatterplot of the data, with the quadratic curve displayed, use a graphing facility to plot the data points and graph the function (with age on the horizontal axis and ratio on the vertical axis).

A forestry commission once sought a way to accurately estimate the weights of trees without having to go through the damaging process of cutting the trees down to weigh them. The weights and trunk girths of 104 tree specimens were measured, in hopes that girth would be useful in predicting weight.

SAS Institute Inc.

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The Tree data set contains data about the weights and trunk girths of 104 tree specimens (eight specimens from each of thirteen rootstocks).

These are the variables in the data set:

This data is sample data from SAS Institute Inc.

It appears that the quadratic model is significant, based on the p-value being less than 0.0001.