Statistical Methods for Testing, Development, and Manufacturing I
Homework #6 - Chapter 11 Regression & Correlation (Montgomery & Runger, 4ed)
1. Use the numbered textbook problems only as references to help add meaning to the data.
2. Do NOT solve the problems as stated in the textbook.
3. Use the methods discussed in class to find the following for each of the numbered problems.
a. Calculate the correlation coefficient r.
b. Determine whether or not there is significant correlation between the variables.
c. Write the regression equation.
d. Use the regression equation to determine the value of Y, given the value of X.
Page 401 #11-6 X = Engine Displacement (cubic inches) Y = Mile per Gallons (mpg)
n Σ X Σ Y Σ X2 Σ Y2 Σ XY
21 5017 620.5 1436737 18986 138663
Predict MPG for an engine displacement of 150 cubic inches.
Answers:
r = - 0.769 t test = - 5.24
t α/2 = ± 2.093
y = 39.2 - 0.0402 x
y = 39.2 - 0.0402 (150) = 33.2 mpg
Page 401 #11-8 X = Sound Pressure Level (dB) Y = Evoked Blood Pressure Rise (mm Hg)
n Σ X Σ Y Σ X2 Σ Y2 Σ XY
20 86 1656 494 140176 7654
Predict Blood Pressure (mmHg) for a Sound Pressure Level of 6.5 dB’s.
Answers:
r = 0.865 t test = 7.314
t α/2 = ± 2.101
y = 64.3 + 4.29 x
y = 64.3 + 4.29 (6.5) = 92 mm Hg
Page 402 #11-11 X = Age (weeks) Y = Strength (psi)
n Σ X Σ Y Σ X2 Σ Y2 Σ XY
20 267 42648 4672 92642656 527620
Predict Strength (psi) for an Age of 18.5 weeks.
Answers:
r = - 0.947 t test = - 12.46
t α/2 = ± 2.101
y = 2625 - 37 x
y = 2625 - 37 (18.5) = 1940.5 psi
4. Rework each of the problems using the “Alternate Form”; of course you should obtain the same results!
Sxx Syy Sxy
# 11-6 238152 651 - 9578
# 11-8 124 3060 +533
# 11-11 1115 1699421 -41200