Question

An article in Electronic Packaging and Production (2002, vol. 42) considered the effect of X-ray inspection of integrated circuits. The radiation dose (rads) were studied as a function of current (in milliamps) and exposure (in minutes).The data arein excel file uploaded to Moodle. Name of the file is “Assignment 4 Data”. Use a software (preferable MINITAB) to answer the following questions.

Part 1. Perform simple linear regression analysis with the variables, radiation dose and exposure time to answer the following questions. (Include the output in your pdf file.)

1. a) Determine response variable and find the fitted line. (Estimated regression line)

2. b) Predict the radiation dose when exposure time is 15 seconds.

3. c) Estimate the standard deviation of radiation dose.

4. d) What percentage of variability in radiation dose can be explained by the

   exposure time?

5. e) Obtain 95% CI for the true slope of regression line.

*****Can you solve the problem above using Minitab and show the steps please?

	X-ray	Inspection	Data
Rads	mA	Exposure 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	30	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

Answer 1

using minitab>stat>Regression>Regreession 'we have

Regression Analysis: Rads versus Exposure Time

Analysis of Variance

Source DF Seq SS Contribution Adj SS Adj MS F-Value P-Value
Regression 1 9403685 71.42% 9403685 9403685 94.94 0.000
Exposure Time 1 9403685 71.42% 9403685 9403685 94.94 0.000
Error 38 3763670 28.58% 3763670 99044
Lack-of-Fit 6 609 0.00% 609 101 0.00 1.000
Pure Error 32 3763062 28.58% 3763062 117596
Total 39 13167355 100.00%

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)
314.713 71.42% 70.66% 4521319 65.66%

Coefficients

Term Coef SE Coef 95% CI T-Value P-Value VIF
Constant -2.2 67.3 (-138.3, 134.0) -0.03 0.974
Exposure Time 68.18 7.00 ( 54.02, 82.35) 9.74 0.000 1.00

Regression Equation

Rads = -2.2 + 68.18 Exposure Time

Fits and Diagnostics for Unusual Observations

Obs Rads Fit SE Fit 95% CI Resid Std Resid Del Resid HI
8 592.0 1361.5 107.0 (1145.0, 1578.0) -769.5 -2.60 -2.83 0.115517
39 1776.0 1020.6 77.7 ( 863.2, 1177.9) 755.4 2.48 2.67 0.060981
40 2368.0 1361.5 107.0 (1145.0, 1578.0) 1006.5 3.40 4.02 0.115517

Obs Cook’s D DFITS
8 0.44 -1.02250 R
39 0.20 0.68022 R
40 0.76 1.45392 R

a) response variable = radiation dose

the fitted line is Rads = -2.2 + 68.18 Exposure Time

b) the radiation dose when exposure time is 15 seconds is -2.2 + 68.18*15 =1020.5

c) the standard deviation of radiation dose. is 314.713

d) 71.42 percentage of variability in radiation dose can be explained by the

exposure time

e) 95% CI for the true slope of regression line is  ( 54.02, 82.35)