The data set kid.weights $($UsingR$)$ contains age, weight, gender and height mea$-$

surements for several children.

$($a$)$ Assume that for all the $5$ years old children, over $50$ pounds consid$-$

ered as overweight. Assume $10\%$ of $5$ years old children are over$-$

weight. Does the data support this assumption? Find a $95\%$ CI for

the mean of weight of all the $5$ years old children and a $90\%$ CI for

the standard deviation of the weight of the $5$ years old children.

$($b$)$ Does the rate of overweight children differ between two genders?

$($c$)$ Fit the first model weight $$ age $+$ height for all ages, make a scat$-$

terplot with a regression line and $95\%$ prediction intervals. Test the

hypothesis that an increase of one inch in height corresponds to a $2-$

pound increase in weight against the alternative that it will increase

by less.

$($d$)$ Fit the second model weight $$ age $+$ height $+$ height$2$ for all the

age, plot the graph of fitted value vs and residuals. Compare with

the first model, which one is better? You can use the adjusted R$2$

for comparison.

$($e$)$ Fit the third model weight $$ age $+$ height $+$ height$2+$ height$3+$

height$4+$height$5.$ Use the partial F$-$test to select between the second

model and the third model $($hint: use anova$()$ function$).$

$($f$)$ Apply AIC on the third model$($hint: use stepAIC$()$ function from

the package MASS$).$ What model is suggested by AIC? For this

model, what is the adjusted R$2?$