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) was determined at different solder temperatures (degrees Celsius). The data for one experiment are given in the table. 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.)

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