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 3.3684x  .01780x2

a. Estimate Y75, the expected viscosity when speed is 75 rpm.

b. What viscosity would you predict for a cone speed of 60 rpm?

c. If
y2 i
8386.43,
yi
210.70,
xiyi
17,002.00, and
x 2 i yi
1,419,780, compute SSE [

y2 i 

ˆ

0
yi 
ˆ

1
xiyi 
ˆ

2
x2 i yi], s2

, and s.

d. From part (c), SST
8386.43  (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
ˆ

2 is s
ˆ 2
.00226, test H0:
2
0 versus Ha:
2 0 at level .01, and interpret the result.