12-25. Reconsider the semiconductor data inExercise 12-7. (a) Test for significa
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Question
12-25. Reconsider the semiconductor data inExercise 12-7.(a) Test for significance of regression using = 0.05. What conclusions can you draw?
(b) Calculate the t-test statistic and P-valuefor each regression coefficient. Using = 0.05, whatconclusions can you draw?
(Montgomery, Douglas C.. Applied Statistics and Probability forEngineers, 4th Edition. John Wiley & Sons, 042006. 12.5).
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Table:
Rads mAmps Exp. Time 7.4 10 0.25 14.8 10 0.5 29.6 10 1 59.2 10 2 88.8 10 3 296 10 10 444 10 15 592 10 20 11.1 15 0.25 22.2 15 0.5 44.4 15 1 88.8 15 2 133.2 15 3 444 15 10 666 15 15 888 15 20 14.8 20 0.25 29.6 20 0.5 59.2 20 1 118.4 20 2 177.6 20 3 592 20 10 888 20 15 1184 20 20 22.2 30 0.25 44.4 30 0.5 88.8 39 1 177.6 30 2 266.4 30 3 888 30 10 1332 30 15 1776 30 20 29.6 40 0.25 59.2 40 0.5 118.4 40 1 236.8 40 2 355.2 40 3 1184 40 10 1776 40 15 2368 40 20
Rads mAmps Exp. Time 7.4 10 0.25 14.8 10 0.5 29.6 10 1 59.2 10 2 88.8 10 3 296 10 10 444 10 15 592 10 20 11.1 15 0.25 22.2 15 0.5 44.4 15 1 88.8 15 2 133.2 15 3 444 15 10 666 15 15 888 15 20 14.8 20 0.25 29.6 20 0.5 59.2 20 1 118.4 20 2 177.6 20 3 592 20 10 888 20 15 1184 20 20 22.2 30 0.25 44.4 30 0.5 88.8 39 1 177.6 30 2 266.4 30 3 888 30 10 1332 30 15 1776 30 20 29.6 40 0.25 59.2 40 0.5 118.4 40 1 236.8 40 2 355.2 40 3 1184 40 10 1776 40 15 2368 40 20
Explanation / Answer
From the statistical software output we get H0: 1=2 =0 H1: Atleast one of the not equal to zero. The Analysis of variance table is follows. Source Degrees of freedom SS MSS F-test Regression 2 11011754 5505877 96.07 Residuals 37 2120556 57312 Total 39 13132310 Source Degrees of freedom SS MSS F-test Regression 2 11011754 5505877 96.07 Residuals 37 2120556 57312 Total 39 13132310F-test statistic is 96.07 F-critical value at 0.05 =3.2519 with 2, 37 degrees of freedom. Rejection region: F >3.2519 our test statistic lies in the rejection region.So we rejectour null hypothesis. b) Predictor Coef SE Coef T P
Constant -429.78 95.33 -4.51 0.000
mAmps 18.380 3.440 5.34 0.000
Exposure time 68.527 5.324 12.87 0.000 The p-value of 2 regression coefficient are 0.000 So we reject our hypothesis in each of the cases. we conclude that the varible gives useful information to thepredictor. The p-value of 2 regression coefficient are 0.000 So we reject our hypothesis in each of the cases. we conclude that the varible gives useful information to thepredictor. Source Degrees of freedom SS MSS F-test Regression 2 11011754 5505877 96.07 Residuals 37 2120556 57312 Total 39 13132310
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