# Question

Use 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 first part of Theorem 14.3 as well as the fact that Yˆ0 and n∑ˆ2σ2 are independent to show that

Is a value of a random variable having the t distribution with n – 2 degrees of freedom.

And the variance

Also, use the first part of Theorem 14.3 as well as the fact that Yˆ0 and n∑ˆ2σ2 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 Questions

Derive a (1 – α) 100% confidence interval for µY|x0, the mean of Y at x = x0, by solving the double inequality –tα/2,n–2 < t < tα/2, n–2 with t given by the formula of Exercise 14.23. Given the joint destiny Find µY|x and µX|y. 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 ...Use the coding of Exercise 14.15 to rework both parts of Exercise 14.42. In exercise When the x’s are equally spaced, the calculation of and can be simplified by coding the x’s by assigning them the values . . . ,- ...With reference to Exercise 14.43, construct a 99% confidence interval for the regression coefficient β. In exercise The following are the scores that 12 students obtained on the midterm and final examinations in a course ...Post your question

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