Microsoft Word - Assignment#4.docx
1.The weight and systolic blood pressure of 26 randomly selected males in the age group 25
to 30 are shown in the following table. Assume that weight and blood pressure are jointly
normally distributed.
Subject Weight
Systolic
BP Subject Weight
Systolic
BP
1 165 130 14 172 153
2 167 133 15 159 128
3 180 150 16 168 132
4 155 128 17 174 149
5 212 151 18 183 158
6 175 146 19 215 150
7 190 150 20 195 163
8 210 140 21 180 156
9 200 148 22 143 124
10 149 125 23 240 170
11 158 133 24 235 165
12 169 135 25 192 160
13 170 150 26 187 159
(a) Find a regression line relating systolic blood pressure to weight.
(b) Test for significance of regression using α = 0.05
(c) Estimate the co
elation coefficient.
2.An engineer at a semiconductor company wants to model the relationship between the
device HFE (y) and three parameters: Emitter-RS (x1), Base-RS (x2), and Emitter-to-
Base RS (x3). The data are shown in the following table.
X1 X2 X3 y X1 X2 X3 y
14.620 XXXXXXXXXX 7.000 XXXXXXXXXX 15.500 XXXXXXXXXX 5.750 97.520
15.630 XXXXXXXXXX 3.375 52.620 16.120 XXXXXXXXXX 3.750 59.060
14.620 XXXXXXXXXX 6.375 XXXXXXXXXX 15.130 XXXXXXXXXX 6.125 XXXXXXXXXX
15.000 XXXXXXXXXX 6.000 98.010 15.630 XXXXXXXXXX 5.375 89.090
14.500 XXXXXXXXXX 7.625 XXXXXXXXXX 15.380 XXXXXXXXXX 5.875 XXXXXXXXXX
15.250 XXXXXXXXXX 6.000 XXXXXXXXXX 14.380 XXXXXXXXXX 8.875 XXXXXXXXXX
16.120 XXXXXXXXXX 3.375 48.140 15.500 XXXXXXXXXX 4.000 66.800
15.130 XXXXXXXXXX 6.125 XXXXXXXXXX 14.250 XXXXXXXXXX 8.000 XXXXXXXXXX
15.500 XXXXXXXXXX 5.000 82.680 14.500 XXXXXXXXXX 10.870 XXXXXXXXXX
15.130 XXXXXXXXXX 6.625 XXXXXXXXXX 14.620 XXXXXXXXXX 7.375 XXXXXXXXXX
(a) Fit a multiple linear regression model to the data.
(b) Predict HFE (y) when x1 = 14.5, x2 = 220, and x3 = 5.0.
Microsoft Word - Assignment#5.docx
Q1
A Six Sigma team is testing pilot test results to see if they have made a ststistically significant improvement.
They need to test this hypothesis statistically and determine the 95% Confidence Interval for the improvement.
Data from the baseline and pilot test are reported in the table below:
Defect
Defects Good Sample Rate
Baseline 6,290 613, XXXXXXXXXX, XXXXXXXXXX
Pilot Test 466 48,534 49, XXXXXXXXXX
Q1.1 State the hypothesis.
Q1.2 Test the hypothesis and state the results in statistical and business statements.
Q1.3 State the 95% confidence interval for the baseline process defect rate in %.
Q1.4 State the 95% confidence interval for the improved process defect rate in %.
Q1.5 Compare the results from the Confidence Interval to the hypothesis test. Do they agree? Why or why not?
Q2.
Conduct a regression analysis for the following data.
Q2.1 Test the hypothesis that X is a good predictor of Y and explain why or why not.
Q2.2 Explain the various parameters of the linear equation.
Q2.3 Explain the strength of the model using the regression model and also using a co
elation analysis.
Q2.4 Show the linear line on the scatter plot graph and the linear equation.
Q2.5 Determine the predicted value of Y given X is 93.1
Q 2.6 Plot the normal probability plot and the residual plot vs X. What do you infer from them?
X Y
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
63.7 4.1
66 -35.2
67.1 -20.3
97.3 -40.3
76.5 0.3
86.1
-16.1
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
Q3
Q3.1 Explain how nuisance (noise) factors can affect data analysis and experiments in the Improve phase.
Q3.2 Explain how you would combat noise when it can be controlled.
Q3.3 Explain how you would combat noise when it can’t be controlled.
Q3.4 Explain how you would use residual analysis in an ANOVA experiment.
Microsoft Word - Assignment#6.docx
1. The following measurements represent the length (in cm) of the electrical contacts
of relays in samples of size 5, taken hourly from the operating process. Create the X-
ar and R charts and decide if the process is in control.
Hour i X1 X2 X3 X4 X5
1 1.9890 2.1080 2.0590 2.0110 2.0070
2 1.8410 1.8900 2.0590 1.9160 1.9800
3 2.0070 2.0970 2.0440 2.0810 2.0510
4 2.0940 2.2690 2.0910 2.0970 1.9670
5 1.9970 1.8140 1.9780 1.9960 1.9830
6 2.0540 1.9700 2.1780 2.1010 1.9150
7 2.0920 2.0300 1.8560 1.9060 1.9750
8 2.0330 1.8500 2.1680 2.0850 2.0230
9 2.0960 2.0960 1.8840 1.7800 2.0050
10 2.0510 2.0380 1.7390 1.9530 1.9170
11 1.9520 1.7930 1.8780 2.2310 1.9850
12 2.0060 2.1410 1.9000 1.9430 1.8410
13 2.1480 2.0130 2.0660 2.0050 2.0100
14 1.8910 2.0890 2.0920 2.0230 1.9750
15 2.0930 1.9230 1.9750 2.0140 2.0020
16 2.2300 2.0580 2.0660 2.1990 2.1720
17 1.8620 2.1710 1.9210 1.9800 1.7900
18 2.0560 2.1250 1.9210 1.9200 1.9340
19 1.8980 2.0000 2.0890 1.9020 2.0820
20 2.0490 1.8790 2.0540 1.9260 2.0080
2. Following is the number of defects in daily samples (n=100) in January. Create the P
and C charts and decide if the process is in control.
Sample Day Number of Defects Sample Day Number of Defects
i Xi i Xi
1 6 16 6
2 8 17 4
3 8 18 6
4 13 19 8
5 6 20 2
6 6 21 7
7 9 22 4
8 7 23 4
9 1 24 2
10 8 25 1
11 5 26 5
12 2 27 15
13 4 28 1
14 5 29 4
15 4 30 1
31 5