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

Question

22. Mist (airborne droplets or aerosols) is generated when metal-removing flulds are used in machining operations soluble oil (cm/sec) and y - the extent of mist droplets having diameters smaller than 10pm (mg/m'): x 89177 189 354 362 442965 to cool and lubricate the tool workpiece. Suppose 7 measures were taken on x- fluld-flow velocity for a 5% 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 regresaion equation is Scatterplot yr y-0.404+ 0.000621x SE Coef T 0.03459 Coef Predictor Constant ? 0.000 D 0.000 B 0.00007579 R-Sqladj)-91.7 Analyais of variance DF Source Regression Residual Error 5 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 varlation can be attributed to the simple linear regression model? investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000. in this way, is there substantial evidence that the true average increase in y is less than When x increases .67 Estimate the true average change in mist associated with a 1 cm/sec Increase in velocity, and do so that conveys information about precision and reliability e) in a way

Explanation / Answer

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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