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).

The least-squares quadratic model is y = 101.4000 + 3.371429x ˆ’ 5.142857x².

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.

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