Provide R code if possible

Question:

A random sample of individuals from a medical centre provided their sex, height

(in m), femur length (in m), and weight (in kg) to a team of medical researchers. The

researchers are interested in how weight varies as a function of height, sex, and femur

length. The assumptions of the multiple linear regression model are deemed reasonable in

this setting. The data are available in the file femur.txt.

a.

Write down a linear model to describe these data using only first-order terms

(no interactions or higher-order effects of the numeric predictors). Be sure to define your

variables and to state all assumptions.

b.

Provide an interpretation of the effect of femur in your model in (a).

c.

Fit the model in (a) and provide the table of parameter estimates, standard

errors, etc.

d.

With reference your output in (c), show that the effect of femur is insignificant

at the 5% level.

e.

Fit the model again, excluding height as a predictor. With reference to your

new summary output, show that femur is significant at the 5% level.

f.

Are your findings in (d) and (e) contradictory? Explain.

g.

Conduct the test of whether sex and femur length have an effect on weight,

after having adjusted for height. In particular:

i.

Specify the null and alternative hypotheses.

ii.

Specify the value of the test statistic.

iii.

Specify the p-value.

iv.

Using a significance level of = 0.05, state your conclusions in the language

of the problem.

h.

Compute the variance inflation factors of the predictors, and explain whether

multicollinearity appears to be a problem in this setting.

Below is data:

Weight Height Femur Sex

221 1.78 0.455 M

228 1.79 0.45 M

194 1.73 0.425 M

209 1.71 0.433 M

203 1.78 0.45 M

167 1.61 0.415 M

233 1.78 0.451 M

215 1.72 0.429 M

204 1.72 0.403 M

198 1.68 0.433 M

214 1.73 0.433 M

232 1.87 0.473 M

219 1.77 0.422 M

218 1.78 0.433 M

145 1.69 0.439 M

226 1.8 0.448 M

185 1.68 0.411 M

241 1.72 0.406 M

208 1.82 0.435 M

198 1.76 0.421 M

228 1.79 0.444 M

253 1.84 0.484 M

188 1.69 0.424 M

179 1.63 0.39 M

181 1.63 0.407 M

207 1.87 0.474 M

212 1.71 0.409 M

227 1.78 0.422 M

193 1.78 0.467 M

198 1.73 0.443 M

212 1.8 0.456 M

280 1.89 0.461 M

235 1.88 0.474 M

257 1.85 0.487 M

206 1.76 0.431 M

221 1.77 0.469 M

210 1.72 0.415 M

151 1.62 0.43 M

268 1.86 0.477 M

179 1.74 0.419 M

207 1.82 0.454 M

187 1.57 0.396 M

167 1.67 0.393 M

240 1.81 0.46 M

203 1.8 0.46 M

225 1.84 0.505 M

138 1.64 0.428 M

205 1.78 0.461 M

234 1.78 0.484 M

144 1.65 0.42 M

178 1.7 0.438 M

273 1.88 0.472 M

211 1.74 0.455 M

154 1.76 0.464 M

192 1.69 0.433 M

155 1.76 0.422 M

228 1.79 0.404 M

264 1.8 0.459 M

278 1.89 0.452 M

104 1.58 0.409 M

192 1.75 0.458 M

181 1.65 0.401 M

152 1.78 0.436 M

246 1.85 0.483 M

126 1.7 0.449 M

145 1.61 0.432 M

206 1.8 0.447 M

247 1.85 0.444 M

219 1.78 0.452 M

182 1.65 0.387 M

183 1.74 0.43 M

169 1.69 0.426 M

226 1.67 0.4 M

280 1.9 0.473 M

215 1.84 0.443 M

239 1.81 0.432 M

220 1.8 0.432 M

185 1.68 0.378 M

182 1.77 0.44 M

173 1.81 0.478 M

186 1.79 0.447 M

211 1.81 0.408 M

159 1.72 0.441 M

307 1.91 0.494 M

214 1.81 0.443 M

246 1.87 0.455 M

199 1.79 0.437 M

170 1.72 0.43 M

217 1.78 0.443 M

231 1.8 0.45 M

195 1.67 0.415 M

154 1.68 0.417 M

270 1.87 0.477 M

149 1.71 0.399 M

176 1.67 0.422 M

221 1.79 0.463 M

176 1.7 0.428 M

269 1.89 0.476 M

203 1.7 0.43 M

179 1.69 0.399 M

228 1.76 0.457 M

177 1.66 0.41 M

194 1.77 0.402 M

179 1.65 0.408 M

219 1.75 0.442 M

165 1.7 0.41 M

204 1.72 0.413 M

193 1.85 0.46 M

187 1.71 0.421 M

210 1.76 0.412 M

163 1.65 0.363 M

110 1.65 0.422 M

223 1.83 0.439 M

207 1.83 0.524 M

164 1.73 0.429 M

180 1.7 0.429 M

206 1.74 0.453 M

198 1.78 0.402 M

236 1.89 0.468 M

132 1.74 0.395 M

242 1.85 0.438 M

251 1.83 0.474 M

201 1.76 0.439 M

228 1.85 0.471 M

207 1.71 0.443 M

118 1.66 0.432 M

136 1.61 0.377 M

220 1.82 0.452 M

137 1.59 0.387 M

194 1.66 0.423 M

226 1.85 0.474 M

235 1.8 0.465 M

229 1.78 0.437 M

164 1.66 0.416 M

267 1.93 0.487 M

186 1.67 0.433 M

167 1.67 0.409 M

171 1.79 0.44 M

155 1.75 0.402 M

178 1.71 0.424 M

162 1.66 0.432 M

185 1.65 0.401 M

156 1.7 0.418 M

162 1.63 0.45 M

201 1.74 0.448 M

188 1.78 0.439 M

189 1.63 0.431 M

212 1.8 0.461 M

177 1.8 0.449 M

163 1.75 0.48 M

147 1.63 0.404 M

241 1.78 0.447 M

216 1.75 0.476 M

165 1.68 0.452 M

148 1.73 0.474 M

163 1.72 0.416 M

236 1.86 0.419 M

175 1.72 0.397 M

177 1.74 0.446 M

181 1.69 0.413 M

155 1.71 0.427 M

163 1.76 0.448 M

164 1.72 0.453 M

167 1.71 0.455 M

178 1.67 0.46 M

160 1.72 0.408 M

173 1.78 0.469 M

166 1.65 0.426 M

194 1.86 0.45 M

220 1.74 0.437 M

192 1.75 0.439 M

226 1.83 0.445 M

207 1.74 0.445 M

215 1.8 0.434 M

141 1.62 0.391 M

201 1.77 0.442 M

250 1.91 0.472 M

197 1.77 0.422 M

212 1.76 0.468 M

124 1.61 0.419 M

185 1.68 0.413 M

243 1.74 0.446 M

224 1.71 0.403 M

225 1.82 0.468 M

181 1.8 0.462 M

181 1.75 0.462 M

209 1.84 0.47 M

190 1.77 0.412 M

215 1.73 0.434 M

171 1.7 0.439 M

163 1.64 0.383 F

120 1.58 0.4 F

176 1.66 0.409 F

171 1.63 0.422 F

189 1.69 0.427 F

149 1.66 0.383 F

202 1.66 0.415 F

156 1.58 0.411 F

111 1.58 0.344 F

114 1.61 0.392 F

147 1.52 0.354 F

113 1.57 0.409 F

155 1.62 0.419 F

146 1.67 0.438 F

148 1.66 0.449 F

132 1.62 0.4 F

80 1.51 0.374 F

121 1.65 0.433 F

143 1.62 0.396 F

130 1.61 0.37 F

164 1.67 0.422 F

95 1.56 0.381 F

98 1.59 0.384 F

182 1.73 0.43 F

156 1.57 0.366 F

108 1.63 0.409 F

139 1.65 0.405 F

102 1.51 0.396 F

126 1.48 0.37 F

138 1.61 0.393 F

135 1.66 0.42 F

61 1.47 0.34 F

122 1.6 0.418 F

81 1.59 0.399 F

178 1.72 0.446 F

126 1.65 0.411 F

149 1.6 0.402 F

127 1.61 0.411 F

165 1.7 0.407 F

120 1.61 0.431 F

123 1.61 0.407 F

82 1.56 0.389 F

165 1.62 0.392 F

155 1.63 0.422 F

163 1.66 0.414 F

92 1.58 0.398 F

180 1.66 0.416 F

152 1.57 0.398 F

151 1.65 0.431 F

97 1.62 0.384 F

96 1.57 0.388 F

112 1.58 0.431 F

142 1.59 0.427 F

117 1.55 0.38 F

142 1.6 0.388 F

155 1.66 0.425 F

221 1.77 0.447 F

90 1.6 0.397 F

125 1.64 0.385 F

140 1.66 0.448 F

157 1.56 0.41 F

131 1.67 0.439 F

126 1.64 0.403 F

106 1.52 0.36 F

164 1.59 0.424 F

165 1.65 0.409 F

135 1.59 0.416 F

106 1.58 0.413 F

138 1.56 0.393 F

72 1.54 0.369 F

162 1.65 0.388 F

140 1.69 0.469 F

130 1.6 0.401 F

89 1.58 0.401 F

179 1.7 0.389 F

146 1.6 0.377 F

123 1.61 0.428 F

102 1.64 0.383 F

88 1.54 0.423 F

93 1.57 0.365 F

132 1.57 0.403 F

120 1.57 0.368 F

166 1.64 0.448 F

93 1.48 0.341 F

128 1.63 0.404 F

155 1.68 0.401 F

130 1.61 0.409 F

68 1.59 0.403 F

91 1.55 0.381 F

135 1.64 0.402 F

124 1.52 0.351 F

169 1.62 0.424 F

117 1.56 0.402 F

150 1.71 0.42 F

147 1.65 0.376 F

137 1.63 0.435 F

102 1.62 0.414 F

90 1.57 0.396 F

221 1.67 0.418 F

120 1.66 0.401 F

95 1.58 0.418 F

135 1.57 0.436 F

145 1.6 0.378 F

143 1.63 0.385 F

139 1.55 0.414 F

113 1.62 0.349 F

98 1.48 0.377 F

113 1.57 0.388 F

95 1.56 0.386 F

160 1.64 0.443 F

125 1.64 0.373 F

176 1.61 0.397 F

102 1.58 0.368 F

155 1.68 0.449 F

132 1.6 0.357 F

76 1.61 0.391 F

202 1.68 0.425 F

129 1.63 0.429 F

116 1.59 0.409 F

153 1.71 0.474 F

105 1.55 0.428 F

172 1.6 0.399 F

184 1.69 0.431 F

206 1.71 0.401 F

187 1.74 0.434 F

105 1.59 0.416 F

113 1.58 0.388 F

107 1.53 0.392 F

221 1.75 0.433 F

127 1.56 0.39 F

195 1.63 0.397 F

135 1.65 0.402 F

200 1.67 0.416 F

182 1.64 0.419 F

95 1.48 0.39 F

199 1.67 0.394 F

104 1.64 0.444 F

107 1.63 0.432 F

106 1.57 0.392 F

126 1.67 0.412 F

170 1.7 0.444 F

139 1.64 0.405 F

112 1.63 0.389 F

180 1.66 0.402 F

133 1.63 0.375 F

163 1.63 0.365 F

114 1.52 0.422 F

162 1.7 0.43 F

109 1.64 0.4 F

134 1.64 0.41 F

189 1.73 0.429 F

151 1.59 0.399 F

199 1.67 0.433 F

180 1.64 0.418 F

151 1.6 0.407 F

148 1.6 0.362 F

124 1.54 0.384 F

187 1.64 0.401 F

86 1.46 0.378 F

157 1.66 0.396 F

85 1.63 0.391 F

146 1.6 0.39 F

98 1.52 0.372 F

121 1.55 0.374 F

124 1.67 0.445 F

152 1.59 0.459 F

103 1.63 0.446 F

100 1.61 0.395 F

93 1.64 0.398 F

115 1.55 0.397 F

85 1.59 0.399 F

134 1.5 0.389 F

160 1.63 0.393 F

170 1.6 0.421 F

136 1.61 0.389 F

154 1.65 0.387 F

180 1.63 0.406 F

203 1.71 0.464 F

149 1.65 0.394 F

113 1.59 0.377 F

105 1.6 0.374 F

168 1.71 0.426 F

152 1.64 0.425 F

161 1.64 0.407 F

175 1.65 0.43 F

117 1.56 0.409 F

169 1.68 0.432 F

75 1.49 0.422 F

183 1.66 0.438 F

187 1.75 0.475 F

112 1.58 0.39 F

148 1.6 0.391 F

137 1.63 0.393 F

144 1.58 0.405 F

174 1.64 0.427 F

144 1.6 0.419 F

195 1.66 0.434 F

218 1.74 0.424 F

125 1.54 0.399 F

110 1.58 0.399 F

173 1.66 0.395 F