Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer Level Packaging Conference, Nov. 3–4, 2005). The failure times of the microchips (in hours) were determined at different solder temperatures (degrees Centigrade). The data for one experiment are given in the table and saved in the WAFER file. The researchers want to predict failure time (y) based on solder temperature (x).

a. Construct a scatterplot for the data. What type of relationship, linear or curvilinear, appears to exist between failure time and solder temperature?

b. Fit the model, E(y) = β0 + β1x + β2x2, to the data. Give the least squares prediction equation.

c. Conduct a test to determine if there is upward curvature in the relationship between failure time and solder temperature. (Use α = .05.)

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