High-alumina refractory castables have been extensively investigated in recent years because of their significant advantages over other refractory brick of the same class-lower production and application costs, versatility, and performance at high temperatures. The accompanying data on x = viscosity (MPa . s) and y = freeflow (%) was read from a graph in the article "Processing of Zero- Cement Self-Flow Alumina Castables" (The Amer. Ceramic Soc. Bull., 1998: 60-66):

The authors of the cited paper related these two variables using a quadratic regression model. The estimated regression function is y = -295.96 + 2.1885x - .0031662x2.
a. Compute the predicted values and residuals, and then SSE and s2.
b. Compute and interpret the coefficient of multiple determination.
c. The estimated SD of b̂2 is sb̂2 = .0004835. Does the quadratic predictor belong in the regression model?
d. The estimated SD of β̂1 is .4050. Use this and the information in (c) to obtain joint CIs for the linear and quadratic regression coefficients with a joint confidence level of (at least) 95%.
e. The estimated SD of µY.400 is 1.198. Calculate a 95% CI for true average free-flow when viscosity = 400 and also a 95% PI for free-flow resulting from a single observation made when viscosity = 400, and compare the intervals.

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x 35 367 373 400 402 456484 y 8 83 79 75 704322