Chapter 13.4, Problem 40E

The article cited in Exercise 49 of Chapter 7 gave summary information on a regression in which the dependent variable was power output (W) in a simulated 200-m race and the predictors were x₁ = arm girth (cm), x₂ = excess post-exercise oxygen consumption (ml/kg), and x₃ = immediate posttest lactate (mmol/L). The estimated regression equation was reported as

y = −408.20 + 14.06x₁ + 0.76x₂ − 3.64x₃ (n = 11, R² = 0.91)

1. a. Carry out the model utility test using a significance level of .01. [Note: All three predictors were judged to be important.]
2. b. Interpret the estimate 14.06.
3. c. Predict power output when arm girth is 36 cm, excess oxygen consumption is 120 ml/kg, and lactate is 10.0.
4. d. Calculate a point estimate for true average power output when values of the predictors are as given in (c).
5. e. Obtain a point estimate for the true average change in power output associated with a 1 mmol/L increase in lactate while arm girth and oxygen consumption remain fixed.