Many studies have researched how traffic load affects road asphalt, but fewer have examined the effect of extreme cold weather. The article “Effects of Large Freeze-Thaw Cycles on Stiffness and Tensile Strength of Asphalt Concrete” (J. Cold Regions Engr. 2016) reports the following data on y = indirect tensile strength (MPa) and x = temperature (°C) for six asphalt specimens in one particular experiment.

a. Verify that a scatterplot of the data is consistent with the choice of a quadratic regression model.
b. Determine the estimated quadratic regression equation.
c. Calculate a point prediction for the indirect tensile strength of this asphalt type at 0°C.

d. What proportion of the observed variation in tensile strength can be attributed to the quadratic regression relationship?

e. Obtain a 95% CI for μ_YΙ0, the true expected tensile strength of this asphalt type at 0°C. 

f. Obtain and interpret a 95% PI at x = 0.

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y -35 -20 -10 0 3.01 3.56 3.47 2.72 10 2.15 22 1.20