Use the formula for t of Exercise 14.28 to show that if the assumptions underlying normal regression analysis are met and β = 0, then R2 has a beta distribution with the mean 1 / n – 1.
Answer to relevant QuestionsBy solving the double inequality –zα/2 ≤ z ≤ zα/2 (with z given by the formula on page 402) for ρ, derive a (1 – α) 100% confidence interval formula for ρ. On page If x01, x02, . . . , x0k are given values of x1, x2, . . . , xk and X0 is the column vector It can be shown that Is a value of a random variable having the t distribution with n- k- 1 degrees of freedom. (a) Show that for k ...The following data pertain to the chlorine residual in a swimming pool at various times after it has been treated with chemicals: (a) Fit a least squares line from which we can predict the chlorine residual in terms of the ...With reference to Exercise 14.44, test the null hypothesis β = 0.350 against the alternative hypothesis β < 0.350 at the 0.05 level of significance. In exercise Raw material used in the production of a synthetic fiber is ...Use the theory of Exercises 14.24 and 14.26, as well as the quantities already calculated in Examples 14.4 and 14.5, to construct (a) A 95% confidence interval for the mean test score of persons who have studied 14 hours ...
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