As a drill bit is used in a manufacturing process, the diameter of the hole that

Question

As a drill bit is used in a manufacturing process, the diameter of the hole that it creates decreases as the number of hours it is used increases. Hole diameter for different hours in use was measured for several different drill bits giving the data below Create a linear model that relates hole diameter to hours of use.

Use this model to predict the number of hours at which the hole diameter would be 5.075mm.

2.383

3.054

5.459

5.828

9.581

10.499

12.426

12.775

13.146

21.903

What percentage of variability is accounted for by your model?

38.6

40.5

60.7

62.0

66.5

67.3

74.3

83.8

92.7

96.2

Time in Use (hours) Hole Diameter (mm) 3.1 5.193 8.2 5.127 17.8 5.028 9 5.123 9.9 5.074 6.6 5.16 14.3 5.044 15.8 5.025 14.6 5.054 3.9 5.165 7 5.156 6.2 5.154 2.9 5.149 19.6 5.01

Explanation / Answer

y =5.21190 -  0.01083 x

hence

at y = 5.075

5.075 =  5.21190 -  0.01083 x

x= (5.21190 -5.075)/0.01083 = 12.64081

hence 12.426 is correct

b) percentage of variability is accounted for by model is given by R^2

=92.65

nearest 92.7 %

SUMMARY OUTPUT Regression Statistics Multiple R 0.962553 R Square 0.926509 Adjusted R Square 0.920385 Standard Error 0.017629 Observations 14 ANOVA df SS MS F Significance F Regression 1 0.047018 0.047018 151.2853 3.67164E-08 Residual 12 0.003729 0.000311 Total 13 0.050747 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.211903 0.009927 525.0103 1.54E-27 5.190273437 5.233532634 5.190273437 5.233533 X Variable 1 -0.01083 0.000881 -12.2998 3.67E-08 -0.01275146 -0.008913658 -0.01275146 -0.00891

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