The viscosity (y) of an oil was measured by a cone and plate viscometer at six different cone speeds (x). It was assumed that a quadratic regression model was appropriate, and the estimated regression function resulting from the n = 6 observations was
y = 2113.0937 + 3.3684x - .01780x2
a. Estimate µY.75, the expected viscosity when speed is 75 rpm.
b. What viscosity would you predict for a cone speed of 60 rpm?
c. If Σ2i - 8386.43, Σyi = 210.70, Σxiyi =17,002.00, and Σxi - yi = 1,419,780, compute SSE and s.
d. From part (c), SST = 8386.432(210.70)2/6 = 987.35. Using SSE computed in part (c), what is the computed value of R2?
e. If the estimated standard deviation of β̂20 at level .01, and interpret the result.