Chapter 12.3, Problem 36E

Misi (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The article “Variables Affecting Mist Generaton from Metal Removal Fluids” (Lubrication Engr., 2002: 10–17) gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 μm (mg/m³):

x	89	177	189	354	362	442	965
y	.40	.60	.48	.66	.61	.69	.99

1. a. The investigators performed a simple linear regression analysis to relate the two variables. Does a scatterplot of the data support this strategy?
2. b. What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist?
3. c. The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a factor of 10 corresponding to the difference between the smallest and largest x values in the sample). When x increases in this way, is there substantial evidence that the true average increase in y is less than .6?
4. d. Estimate the true average change in mist associated with a 1 cm/see increase in velocity, and do so in a way that conveys information about precision and reliability.