(airborne droplets or aerosols) is generated when metal-removing fluids are used
ID: 2949461 • Letter: #
Question
(airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool workpiece. Suppose 7 measures were taken on x-fluid-flow velocity for a 5% soluble oll (cm/sec) and y - the extent of mist droplets having diameters smaller than 10pm (mg/m2) 22. Mist 89 177 189 354 362 442 965 0.40 0.60 0.48 0.66 0.61 0.69 0.99 Using Minitab we generate an scatterplot and the regression analysis output Regression Analysis: y versus x The regression equation is Scatter plat ofyn ?" ?. 404 + 0.000621x Coef SE Coef T P Predictor Constant 0.03459 B 0.00007579 ? 0.000 D 0.000 R-Sq(adj) -91.7 Analysis of variance MS Source Regreasion Residual Error5 Total 1 0.19614 0.19614 67.15 0.000 G 0.00292 6 0.21074 a) Obtain the values of A, B, C, D, E, F, and G. b) Does the scatterplot of the data support a linear relationship between x and y? Explain. c) What proportion of mist variation can be attributed to the simple linear regression model? d) The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000. When x increases in this way, is there substantial evidence that the true average increase in y is less than .67 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 rellability e)Explanation / Answer
SolutionA:
From regression output
y=0.404+0.000621x
A=yintercept=0.404
B=slope=0.000621
C=t test for intercept=coefficient of constant/std error of const
=0.404/0.03459
=11.67968
C=11.67968
D=t test for slope=coeff/stderrro
=0.000621/0.00007579
D=8.193693
E=0.054045
F=R sq=SSR/SST=0.19614/0.21074=0.9307=0.9307*100=93.07%
G=SSE=SST-SSR=0.21074-0.19614=0.0146
Solutionb:
Yes from scaterplot we observe there is positive linear relationship between x and y
also r=correlation coefficient=sqrt(R sq)
r=sqrt(0.9307
r=0.9647
From Linear:
strength:strong
Direction :postive
Solutionc:
From output R sq=coeffcient of determination=0.9307
=0.9307*100
m=93.07%
Intrepretation:
93.07% variation in y is explained by model.Good model.
93.07% variation can be attributed to simple linear regression model.
Solutiond:
Slope=change in Y/Change in X
slope=change inY/1000-100
0.000621=change in Y/900
change in Y=0.000621*900
change in Y=0.5589
which is less than 0.6
YES,there is substantial evidence that the true avergae increase in y is less than 0.6
SolutionE:
true average change in mist
slope=true average change in mist/change in velocity
0.00621=true average change in mist/1
given velocity=1 cm/sec
The true average change in mist associated with a 1 cm/sec increase in velocity is 0.00621
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