Use the result of part(b) of exercise 14.20 to show that
Is a value of a random variable having the standard normal distribution. Also, use the first part of Theorem 14.3 and the fact that A and n∑2/σ2 are independent to show that
Is a value of a random variable having the t distribution with n – 2 degrees of freedom.
Answer to relevant QuestionsUse the results of Exercises 14.20 and 14.21 and the fact that E(Bˆ) = β and var(Bˆ) = σ2/ Sxx to show that Yˆ0 = Aˆ + Bˆ is a random variable having a normal distribution with the mean And the variance Also, use the ...Use the formula for t of Exercise 14.28 to derive the following (1 – α) 100% confidence limits for β: In exercise Use the t statistic of Theorem 14.8 to construct a (1 – α)100% confidence interval formula for βi for i = 0, 1, . . . , k. Theorem 14.8 Under the assumptions of normal multiple regression analysis, Are values of random ...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 ...The following table shows the assessed values and the selling prices of eight houses, constituting a random sample of all the houses sold recently in a metropolitan area: (a) Fit a least squares line that will enable us to ...
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