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Statistics / Applied Statistics and Probability for Engineers 6 / Chapter 12.1 / Problem 12E

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

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The pull strength of a wire bond is an important

Chapter 12, Problem 12E

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QUESTION:

The pull strength of a wire bond is an important characteristic. Table E12-4 gives information on pull strength (y) die height \(\left(\mathrm{x}_{1}\right)\), post height \(\left(\mathrm{x}_{2}\right)\), loop height \(\left(\mathrm{x}_{3}\right)\) wire length \(\left(\mathrm{x}_{4}\right)\) bond width on the die \(\left(\mathrm{x}_{5}\right)\) , and bond width on the post \(\left(\mathrm{x}_{6}\right)\) .

Fit a multiple linear regression model using \(\mathrm{x}_{2}, \mathrm{x}_{3}, \mathrm{x}_{4}, \text { and } \mathrm{X}_{5}\) as the regressors Estimate \(\sigma^{2}\).Find the se \(\left(\widehat{\beta}_{j}\right)\). How precisely are the regression coefficients estimated in your opinion? Use the model from part () a to predict pull strength when \(x_{2}=20, x_{3}=30, x_{4}=90, \text { and } x_{3}=2.0\)

Equation Transcription:

$(y)$

$({x}_{1})$

$({x}_{2})$

$({x}_{3})$

$({x}_{4})$

$({x}_{5})$

$({x}_{6})$

${x}_{2},\ {x}_{3},\ {x}_{4},\ and\ {x}_{5}$

${\sigma{}}^{2}$

$(\ \widehat{\beta{}}{\ }_{j})$

${x}_{2}=20,\ {x}_{3}=30,\ {x}_{4}=90\ and\ {x}_{3}=2.0$

Text Transcription:

(y)

(x1)

(x2)

(x3)

(x4)

(x5)

(x6)

x2, x3, x4, and x5

\sigma^2

\widehat \beta_j

x2=20, x3=30, x4=90 and x3=2.0

Questions & Answers

QUESTION:

The pull strength of a wire bond is an important characteristic. Table E12-4 gives information on pull strength (y) die height \(\left(\mathrm{x}_{1}\right)\), post height \(\left(\mathrm{x}_{2}\right)\), loop height \(\left(\mathrm{x}_{3}\right)\) wire length \(\left(\mathrm{x}_{4}\right)\) bond width on the die \(\left(\mathrm{x}_{5}\right)\) , and bond width on the post \(\left(\mathrm{x}_{6}\right)\) .

Fit a multiple linear regression model using \(\mathrm{x}_{2}, \mathrm{x}_{3}, \mathrm{x}_{4}, \text { and } \mathrm{X}_{5}\) as the regressors Estimate \(\sigma^{2}\).Find the se \(\left(\widehat{\beta}_{j}\right)\). How precisely are the regression coefficients estimated in your opinion? Use the model from part () a to predict pull strength when \(x_{2}=20, x_{3}=30, x_{4}=90, \text { and } x_{3}=2.0\)

Equation Transcription:

$(y)$

$({x}_{1})$

$({x}_{2})$

$({x}_{3})$

$({x}_{4})$

$({x}_{5})$

$({x}_{6})$

${x}_{2},\ {x}_{3},\ {x}_{4},\ and\ {x}_{5}$

${\sigma{}}^{2}$

$(\ \widehat{\beta{}}{\ }_{j})$

${x}_{2}=20,\ {x}_{3}=30,\ {x}_{4}=90\ and\ {x}_{3}=2.0$

Text Transcription:

(y)

(x1)

(x2)

(x3)

(x4)

(x5)

(x6)

x2, x3, x4, and x5

\sigma^2

\widehat \beta_j

x2=20, x3=30, x4=90 and x3=2.0

ANSWER:

Problem 12E

The pull strength of a wire bond is an important characteristic. The following table gives information on pull strength, die height , post height ,loop height , wire length , bond width on the die , and bond width on the post .

(a) Fit a multiple linear regression model using as the regressors

(b) Estimate.

(c) Find the . How precisely are the regression coefficients estimated in your opinion?

(d) Use the model from part (a) to predict pull strength when.

Step by Step Solution

Step 1 of 6

Consider the following variables,

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