The following data were collected in an experiment to study the relationship between the speed of a cutting tool in m/s (x ) and the lifetime of the tool in hours (y).
|
x
|
1
|
1.5
|
2
|
2.5
|
3
|
|
y
|
99
|
96
|
88
|
76
|
66
|
The least-squares quadratic model is y = 101.4000 + 3.371429x - 5.142857x 2 .
a. Using this equation, compute the residuals.
b. Compute the error sum of squares SSE and the total sum of squares SST.
c. Compute the error variance estimate s2 .
d. Compute the coefficient of determination R2 .
e. Compute the value of the F statistic for the hypothesis H0 : β1 = β2 = 0. How many degrees of freedom does this statistic have?
f. Can the hypothesis H0 : β1 = β2 = 0 be rejected at the 5% level? Explain.