A mechanical engineer is investigating the surface finish of metal parts produced on a lathe and its relationship to the speed (in revolutions per minute) and type of cutting tool of the lathe. The data are shown in Table 6-14.

(a) Build a regression model using indicator variables and comment on the significance of regression.

(b) Build a separate model for each tool type and comment on the significance of regression of each model

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Observation Surface Finish Type of Cutting Observation Surface Finish Type of Cutting Number, i Yi RPM Tool Number, i Yi RPM Tool 1 45.44 225 302 11 33.50 224 416 2 42.03 200 302 12 31.23 212 416 3 50.10 250 302 13 37.52 248 416 4 48.75 245 302 14 37.13 260 416 199 5 47.92 235 302 15 34.70 243 416 6 47.79 237 302 16 33.92 238 416 7 52.26 265 302 17 32.13 224 416 8 50.52 259 302 18 35.47 251 416 10 96 45.58 221 302 19 33.49 232 416 44.78 218 302 20 32.29 216 416