The Viscosity (Y) of an Oil Was Measured by a Cone

Essay

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 $y = - 113.0937 + 3.3684 x - .01780 x ^ { 2 }$
a. Estimate $\mu _ { y .75 }$
, the expected viscosity when speed is 75 rpm.
b. What viscosity would you predict for a cone speed of 60 rpm.
c. If $\Sigma y _ { i } ^ { 2 } = 8386.43 , \Sigma y _ { i} = 210.70 , \Sigma x _ { i } y _ { i } = 17,002.00$
and $\Sigma x _ { i} ^ { 2 } y _ { i } = 1,419,780$
compute SSE $\text { [Recall that } \left. S S S = \Sigma y _ { i } ^ { 2 } - \hat { \beta } _ { 0 } \Sigma y _ { i } - \hat { \beta }_1 \Sigma x _ { i } y _ { i } - \hat { \beta } _ { 2 } \Sigma x _ { i } ^ { 2 } y _ { i } \right] , \quad s ^ { 2 } \text {, and s. }$
d. From part ( c ), $\operatorname { SST } = 8386.43 - ( 210.70 ) ^ { 2 } / 6 = 987.35 .$
Using SSE computed in part ( c ), what is the computed value of $R ^ { 2 } ?$
e. If the estimated standard deviation of
at level .01.