The estimates of β 0 and β 1 .

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 12.3, Problem 7AYU

a.

To determine

To find: The estimates of β0 and β1 .

b.

To determine

To compute: The standard error and the point estimate for σ .

c.

To determine

The value of sb1 .

d.

To determine

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

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Question 4 An article in Quality Progress (May 2011, pp. 42-48) describes the use of factorial experiments to improve a silver powder production process. This product is used in conductive pastes to manufacture a wide variety of products ranging from silicon wafers to elastic membrane switches. Powder density (g/cm²) and surface area (cm/g) are the two critical characteristics of this product. The experiments involved three factors: reaction temperature, ammonium percentage, stirring rate. Each of these factors had two levels, and the design was replicated twice. The design is shown in Table 3. A222222222222233 Stir Rate (RPM) Ammonium (%) Table 3: Silver Powder Experiment from Exercise 13.23 Temperature (°C) Density Surface Area 100 8 14.68 0.40 100 8 15.18 0.43 30 100 8 15.12 0.42 30 100 17.48 0.41 150 7.54 0.69 150 8 6.66 0.67 30 150 8 12.46 0.52 30 150 8 12.62 0.36 100 40 10.95 0.58 100 40 17.68 0.43 30 100 40 12.65 0.57 30 100 40 15.96 0.54 150 40 8.03 0.68 150 40 8.84 0.75 30 150…

- + ++ Table 2: Crack Experiment for Exercise 2 A B C D Treatment Combination (1) Replicate I II 7.037 6.376 14.707 15.219 |++++ 1 བྱ॰༤༠སྦྱོ སྦྱོཋཏྟཱུ a b ab 11.635 12.089 17.273 17.815 с ас 10.403 10.151 4.368 4.098 bc abc 9.360 9.253 13.440 12.923 d 8.561 8.951 ad 16.867 17.052 bd 13.876 13.658 abd 19.824 19.639 cd 11.846 12.337 acd 6.125 5.904 bcd 11.190 10.935 abcd 15.653 15.053 Question 3 Continuation of Exercise 2. One of the variables in the experiment described in Exercise 2, heat treatment method (C), is a categorical variable. Assume that the remaining factors are continuous. (a) Write two regression models for predicting crack length, one for each level of the heat treatment method variable. What differences, if any, do you notice in these two equations? (b) Generate appropriate response surface contour plots for the two regression models in part (a). (c) What set of conditions would you recommend for the factors A, B, and D if you use heat treatment method C = +? (d) Repeat…

Question 2 A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to nonrecoverable failure. A test is run at the parts producer to determine the effect of four factors on cracks. The four factors are: pouring temperature (A), titanium content (B), heat treatment method (C), amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm x10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown in Table 2. 1 (a) Estimate the factor effects. Which factor effects appear to be large? (b) Conduct an analysis of variance. Do any of the factors affect cracking? Use a = 0.05. (c) Write down a regression model that can be used to predict crack length as a function of the significant main effects and interactions you have identified in part (b). (d) Analyze the residuals from this experiment. (e) Is there an…

Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 12.3, Problem 7AYU

a.

To determine

To find: The estimates of β0 and β1 .

b.

To determine

To compute: The standard error and the point estimate for σ .

c.

To determine

The value of sb1 .

d.

To determine

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 12.3, Problem 7AYU

a.

To determine

To find: The estimates of β0 and β1 .

b.

To determine

To compute: The standard error and the point estimate for σ .

c.

To determine

The value of sb1 .

d.

To determine

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

Expert Solution & Answer

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 12.3, Problem 7AYU

a.

To determine

To find: The estimates of β0 and β1 .

b.

To determine

To compute: The standard error and the point estimate for σ .

c.

To determine

The value of sb1 .

d.

To determine

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

Expert Solution & Answer

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Answer 5

Chapter 12.3, Problem 7AYU

a.

To determine

To find: The estimates of β0 and β1 .

b.

To determine

To compute: The standard error and the point estimate for σ .

c.

To determine

The value of sb1 .

d.

To determine

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

Answer 6

Chapter 12.3, Problem 7AYU

a.

To determine

To find: The estimates of β0 and β1 .

Answer 7

Chapter 12.3, Problem 7AYU

a.

To determine

To find: The estimates of β0 and β1 .

Answer 8

b.

To determine

To compute: The standard error and the point estimate for σ .

Answer 9

b.

To determine

To compute: The standard error and the point estimate for σ .

Answer 10

c.

To determine

The value of sb1 .

Answer 11

c.

To determine

The value of sb1 .

Answer 12

d.

To determine

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

Answer 13

d.

To determine

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

Answer 14

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Answer 15

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Answer 16

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Answer 17

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The estimates of β 0 and β 1 .

Solution Summary: The author explains the least-square regression equation for the data from Section 4.2, which is stackrely=2.2x+1.2.

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To find: The estimates of β0 and β1 .

To compute: The standard error and the point estimate for σ .

The value of sb1 .

To test: H0:β1=0 versus H1:β1≠0 at the α=0.05 significance level by assuming that the residuals are normally distributed.

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Chapter 12 Solutions