The data set kid.weights 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

$2$

$?$Using R to solve