Failure times of silicon wafer microchips. Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer...

Failure times of silicon wafer microchips. Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer Level Packaging Conference, November 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 next table (p. 208). 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.)