Failure times of silicon wafer microchips. Refer to the National Semiconductor study of manufactured silicon wafer integrated circuit chips, Exercise 12.78 (p. 725). Recall that the failure times of the microchips (in hours) were determined at different solder temperatures (degrees Celsius).

The data are repeated in the table in the next column.

a. Fit the straight-line model E1y2 = b0 + b1x to the data, where y = failure time and x = solder temperature.

b. Compute the residual for a microchip manufactured at a temperature of 152°C.

c. Plot the residuals against solder temperature (x). Do you detect a trend?

d. In Exercise 12.78c, you determined that failure time (y)

and solder temperature (x) were curvilinearly related.

Does the residual plot, part

c, support this conclusion?

Temperature (°C) Time to Failure (hours)
165 200 162 200 164 1,200 158 500 158 600 159 750 156 1,200 157 1,500 152 500 147 500 149 1,100 149 1,150 142 3,500 142 3,600 143 3,650 133 4,200 132 4,800 132 5,000 134 5,200 134 5,400 125 8,300 123 9,700