Mist (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 y 89 177 189 354 362 442 965 .40 .60 .48 .66 .61 .69 .99 a. The investigators performed a simple linear regres- sion analysis to relate the two variables. Does a scat- terplot of the data support this strategy? b. What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? 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 sub- stantial evidence that the true average increase in y is less than .6? d. Estimate the true average change in mist associated with a 1 cm/sec increase in velocity, and do so in a way that conveys information about precision and reliability.
Mist (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 y 89 177 189 354 362 442 965 .40 .60 .48 .66 .61 .69 .99 a. The investigators performed a simple linear regres- sion analysis to relate the two variables. Does a scat- terplot of the data support this strategy? b. What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? 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 sub- stantial evidence that the true average increase in y is less than .6? d. Estimate the true average change in mist associated with a 1 cm/sec increase in velocity, and do so in a way that conveys information about precision and reliability.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcribed Image Text:Mist (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
y
89 177 189 354 362 442 965
.40 .60 .48 .66 .61 .69 .99
a. The investigators performed a simple linear regres-
sion analysis to relate the two variables. Does a scat-
terplot of the data support this strategy?
b. What proportion of observed variation in mist can be
attributed to the simple linear regression relationship
between velocity and mist?
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 sub-
stantial evidence that the true average increase in y is
less than .6?
d. Estimate the true average change in mist associated
with a 1 cm/sec increase in velocity, and do so in a
way that conveys information about precision and
reliability.
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