A mechanical engineer is investigating the thickness of the surface finish (measured in mm) of metal parts produced on a lathe and its relationship to the speed (in revolutions per minute) of the lathe. The metal parts can also be cut using two types of cutting tools (called Type *302" and "416", respectively). A sample of 10 metal parts from each type of cutting tool is sampled, along with the corresponding lathe speed. A scatterplot of the dataset is given below: Surface finish (in mm) versus lathe speed (rpm) for tool types 302 (circles) and 416 (crosses) Surface Finish (mm) 200 210 220 230 240 250 260 Lathe Speed (rpm) For completeness, the full dataset is provided via the code below which you can copy-and- paste into RStudio (if you wish): SurfaceFinish = c (45.44, 42.03, 50.10, 48. 75, 47.92, 47.79, 52.26, 50.52, 45.58, 44.78, 33.50, 31.23, 37.52, 37.13, 34.70, 33. 92, 32 .13, 35. 47, 33.49, 32.29) LatheSpeed = c(225, 200, 250, 245, 235, 237, 265, 259, 221, 218, 224, 212, 248, 260, 243, 238, 224, 251, 232, 216) Type = c(rep ("302", 10), rep("416",10) ) Type = as . factor (Type) A multiple linear regression model with inferations was fit to these data, with the results summarised in the computer output: Coefficients: Estimate Std. Error t value pr ()It1) (Intercept) 11.503 2.504 LatheSpeed 0.153 0 . 011 Type416 -6.094 4. 025 LatheSpeed : Type416 -0.031 0. 017 Residual standard error: 0.6371 on 16 degrees of freedom Multiple R-squared: 0.9936, Adjusted R-squared: 0. 9924