The data set kid.weights (Library: UsingR) contains age, weight, and height measurements for several children.

age weight height gender

1583838M

21038743M

3875048M

41389861M

5824747F

6523024F

7282429M

8794548F

910714459M

10452424M

11584040F

1261527M

1372026F

1431029F

1581929F

16112928F

171288059M

18112028F

19142830F

20112424M

21523536M

22523036M

23645247F

241077248F

25442833M

2641423M

2761828F

2851125M

29353135M

30352834M

31463132F

3261425F

33343840F

3451523M

35122733F

36626036F

37704036M

38604040F

39222131M

40654739F

41514641F

42183033F

431396958M

441247653F

4571631F

4651123F

47283833F

48252534M

49432936M

5082121F

51843648F

52482838M

53634136F

5441312M

55102127F

56263324M

57594024F

58233236F

59332736M

60162026M

61393038M

62564540M

63233424M

6481928M

65634136F

66414030F

6781927F

6871424M

69484341M

701049033F

71494545F

72152930F

7313010558M

741119448M

7572226F

76736936F

7751725M

78372732F

7931223F

80614040F

81302524F

8241325M

8382027F

8441628M

85484537M

86182726F

8792025F

88785446M

89726038M

90333031M

9151830F

92775552F

9351423F

94443424F

95644553F

96734848M

97363036M

98222532F

99553836M

10031324F

101112229F

10281928F

103 1247454M

104503036M

105 1178950F

106693542F

107393334M

108 1417855M

109424330F

110714034M

111553239M

112393137M

11371524M

11471922M

115 1115558F

116364035M

117333738M

118233430F

119964545M

120794448F

121715046F

122655047M

123142832F

124453235F

125202224M

126655249F

127464048F

128604240F

129132228F

130142332M

13181628F

13241722F

133483040F

134684038M

135293232M

13672629F

137193033M

138 1086153F

139 1316554F

140755248M

141202337M

142212931F

14371828M

144413238M

145 1135054F

14631324F

147733643M

148774750M

149 1308061M

150102330M

151 1426461M

152694547M

153212540F

154916548F

155272633M

156383838M

157152030F

158 13315059M

159614242M

160665348F

161783536F

16251626F

163 13915067M

164422529M

165403024F

166985241F

167362738F

168342736M

169192234F

170263031M

171603536M

172784251M

17331223F

174744750F

17571426M

176393239M

177312530F

178 1269358F

179313035F

180 1425950M

181 14410060F

182473442F

183835247F

184614343F

185563236F

18661324M

187151824M

188363838F

18931727F

190674648F

191272934F

192 1015050M

19331425M

19431324M

195312626M

19651123F

197443239M

198 1017045F

19951626F

200875042M

201182633F

202172331F

203463741F

204 1156054F

205944551F

206222634F

207 12613159M

208162223F

20941223F

210 1437056M

211 1308658F

212313536M

21331424F

214 1398558M

215 1055852F

216252834F

217121722M

218473436M

21951924F

22051322F

221111829F

222222331M

223101723M

224463036F

225534143M

226493033F

22731322M

228 12512549F

229513239M

23081828M

231143536M

232393239M

233 12910861M

234604039F

235534230M

236402836F

237252636M

238262626M

239262329M

240744245F

241122832M

242695543M

243 1266536F

244 1138056F

245644940M

246101827F

24751425M

248232633M

249 1228540M

25051427M

(a) Fit the linear model shown below and report summary of the model.

weight = b₀ + b₁age + b₂height + b₃height² + b₄height³ + b₅height⁴

(b) Use the partial F-test to select between this model and the nested models found by using only first-, second-, and third-degree polynomials for height.