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

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