22. Mist (airborne droplets or aerosols) is generated when metal-removing fluids

Question

22. Mist (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 ol (cm/sec) and y the extent of mist droplets having diameters smaller than 10pm (mg/m2 89 177 189354 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 analysls output. Regression Analysis: y versus x The regression equation is y-0.404+ 0.000621x Predictor Constant CoefSE Coef ?. 03459 ? 0.00007579 ? 0.000 D 0.000 R-9q(adj) -91.7 Analyais of variance Source Regression Residual Error5 Total DF 8S MS 1 0.19614 0.19614 67.15 0.000 G 0.00292 6 0.21074 a) Obtaln the values of A, B, C, D, E, F, and G b) Does the scatterplot of the data support a linear relationshlp between x and y? Explain c) What proportion of mist varlation 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 .6? e) 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

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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