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Chapter 12: Q-129E (page 708)

Failure times of silicon wafer microchips. Refer to the National Semiconductor study of manufactured silicon wafer integrated circuit chips, Exercise 12.63 (p. 749). Recall that the failure times of the microchips (in hours) was determined at different solder temperatures (degrees Celsius). The data are repeated in the table below.

  1. Fit the straight-line modelto the data, where y = failure time and x = solder temperature.
  2. Compute the residual for a microchip manufactured at a temperature of 149°C.
  3. Plot the residuals against solder temperature (x). Do you detect a trend?
  4. In Exercise 12.63c, you determined that failure time (y) and solder temperature (x) were curvilinearly related. Does the residual plot, part c, support this conclusion?

Short Answer

Expert verified

a) From the excel output below, the straight-line model for y on x can be written as E(y) = 30855.91-191.567x.

b) Residual value; ε = (2312.427-1,100) = 1212.427

c) From the excel output, the residual plot denotes a curvilinear relationship amongst the residuals against solder temperature (x).

d) From the graph, it can be concluded that there exists a curvilinear relationship between failure time (y) and solder temperature (x) as the residual plot indicates a curvilinear relationship.

Step by step solution

01

Straight-line model

From the excel output below, the straight-line model for y on x can be written as E(y) = 30855.91-191.567x.

02

Prediction value

The residual for a microchip manufactured at a temperature of 149°C can be computed using

ε=y∧-yforx=149,y=1,100andy∧=30855.91-191.567y∧=2312.427

Therefore ε = (2312.427-1,100) = 1212.427

03

Residual plot

From the excel output, the residual plot denotes a curvilinear relationship amongst the residuals against solder temperature (x).

04

Residual plot interpretation

From the graph, it can be concluded that there exists a curvilinear relationship between failure time (y) and solder temperature (x) as the residual plot indicates a curvilinear relationship.

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Most popular questions from this chapter

Personality traits and job performance. When attempting to predict job performance using personality traits, researchers typically assume that the relationship is linear. A study published in the Journal of Applied Psychology (Jan. 2011) investigated a curvilinear relationship between job task performance and a specific personality trait—conscientiousness. Using data collected for 602 employees of a large public organization, task performance was measured on a 30-point scale (where higher scores indicate better performance) and conscientiousness was measured on a scale of -3 to +3 (where higher scores indicate a higher level of conscientiousness).

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SSE = 160.44.

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