Exercise 49 in Chapter 7 refers to an article that provides information on a regression analysis. The regression model examines the relationship between power output in a simulated 200-m race and three predictors: arm girth, excess post-exercise oxygen consumption, and immediate posttest lactate. The estimated regression equation is given. In this exercise, we will perform a model utility test to determine the significance of the predictors.
To test the utility of the regression model, we need to determine if the predictors are significant. The null hypothesis states that all three regression coefficients are equal to zero, while the alternative hypothesis states that at least one coefficient is not equal to zero. With a significance level of 0.01, we calculate the test statistic using the formula F = (R^2/k) / ((1-R^2)/(n-k-1)). Substituting the given values, we find that the test statistic is 23.6. By comparing this value to the critical value from the F-distribution table, we find that 23.6 is greater than 8.45. Therefore, we reject the null hypothesis and conclude that at least one predictor is significant in the regression model.