a) Test for main effects and interactions using Wilks statistics and Lawley-Hotelling.

(b) If we reject the null hypothesis in one of the tests performed in (a), conduct an F test

for each variable y _i . What conclusions to draw?

(c) Test the significance of each variable by adjusting for the other three variables.

(d) Use contrasts to compare methods 2 vs. 1 and 3, and 2 vs. 1 and 4

Table 6.18. Snapbean Data S V 1 Y2 Y3 Y4 S V 1 Y2 Y4 1 1 3 1 1 2 3 4 5 295 302 318 345 325 275 290 295 296 1 2 3 4 5 1 2 3 4 5 3.4 2.9 3.3 3.1 3.3 3.6 1 2 3 2 3.9 3.7 3.7 4.1 330 299 1 3 3 3 315 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 3 4 5 59.3 60.3 60.9 60.6 60.4 59.3 59.4 60.0 58.9 59.5 59.4 60.2 60.7 60.5 60.1 63.7 64.1 63.4 63.2 63.2 60.6 61.0 60.7 60.6 60.3 63.8 63.2 63.3 63.2 63.1 4.5 4.5 5.3 5.8 6.0 6.7 4.8 5.1 5.8 4.8 5.1 5.3 6.4 7.1 7.8 5.4 5.4 5.4 5.3 5.0 6.8 6.5 6.8 7.1 6.0 5.7 6.1 6.0 5.9 5.4 38.4 38.6 37.2 38.1 38.8 37.9 36.6 38.7 37.5 37.0 38.7 37.0 37.4 37.0 36.9 39.5 39.2 39.0 39.0 39.0 38.1 38.6 38.8 38.6 38.5 40.5 40.2 40.0 40.0 39.7 m+na+m+m+in+ 68.1 68.0 68.5 68.6 68.6 64.0 63.4 63.5 63.4 63.5 68.0 68.7 68.7 68.4 68.6 69.8 69.5 69.5 69.9 70.3 66.6 66.5 67.1 65.8 65.6 70.1 72.3 69.7 69.9 69.8 42.2 42.4 41.5 41.9 42.1 40.9 41.4 41.6 41.4 41.1 42.3 41.6 40.7 42.0 42.4 48.4 47.8 46.9 47.5 47.1 45.7 46.8 46.3 46.3 46.1 48.1 47.8 46.7 47.1 46.7 304 302 308 271 284 281 291 270 248 2 280 284 286 284 268 233 248 244 266 244 293 284 277 299 285 265 247 231 268 247 205 239 230 235 220 253 249 226 248 236 1 4 1 3.7 3.5 3.8 3.5 3.4 1.4 1.3 1.3 1.3 1.1 1.8 1.7 1.7 1.8 1.9 1.7 0.7 1.5 1.3 1.4 2 2 4. 2 3 4 5 1 2 3 4 5 2 264 2 3 1 4 3 257 260 261 282 284 291 299 295 2 2 3 4 5 3 4 5 Table 6.18. Snapbean Data S V 1 Y2 Y3 Y4 S V 1 Y2 Y4 1 1 3 1 1 2 3 4 5 295 302 318 345 325 275 290 295 296 1 2 3 4 5 1 2 3 4 5 3.4 2.9 3.3 3.1 3.3 3.6 1 2 3 2 3.9 3.7 3.7 4.1 330 299 1 3 3 3 315 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 3 4 5 59.3 60.3 60.9 60.6 60.4 59.3 59.4 60.0 58.9 59.5 59.4 60.2 60.7 60.5 60.1 63.7 64.1 63.4 63.2 63.2 60.6 61.0 60.7 60.6 60.3 63.8 63.2 63.3 63.2 63.1 4.5 4.5 5.3 5.8 6.0 6.7 4.8 5.1 5.8 4.8 5.1 5.3 6.4 7.1 7.8 5.4 5.4 5.4 5.3 5.0 6.8 6.5 6.8 7.1 6.0 5.7 6.1 6.0 5.9 5.4 38.4 38.6 37.2 38.1 38.8 37.9 36.6 38.7 37.5 37.0 38.7 37.0 37.4 37.0 36.9 39.5 39.2 39.0 39.0 39.0 38.1 38.6 38.8 38.6 38.5 40.5 40.2 40.0 40.0 39.7 m+na+m+m+in+ 68.1 68.0 68.5 68.6 68.6 64.0 63.4 63.5 63.4 63.5 68.0 68.7 68.7 68.4 68.6 69.8 69.5 69.5 69.9 70.3 66.6 66.5 67.1 65.8 65.6 70.1 72.3 69.7 69.9 69.8 42.2 42.4 41.5 41.9 42.1 40.9 41.4 41.6 41.4 41.1 42.3 41.6 40.7 42.0 42.4 48.4 47.8 46.9 47.5 47.1 45.7 46.8 46.3 46.3 46.1 48.1 47.8 46.7 47.1 46.7 304 302 308 271 284 281 291 270 248 2 280 284 286 284 268 233 248 244 266 244 293 284 277 299 285 265 247 231 268 247 205 239 230 235 220 253 249 226 248 236 1 4 1 3.7 3.5 3.8 3.5 3.4 1.4 1.3 1.3 1.3 1.1 1.8 1.7 1.7 1.8 1.9 1.7 0.7 1.5 1.3 1.4 2 2 4. 2 3 4 5 1 2 3 4 5 2 264 2 3 1 4 3 257 260 261 282 284 291 299 295 2 2 3 4 5 3 4 5