Homework 4

1.（10）使用R构造矩阵X和Y，然后在新观测值X1 = 4，X2 = 81和X3 =时计算残差的方差-协方差矩阵和均值响应∑ {b}。 43。矩阵的尺寸是多少？

2.（10）提及问题，当有两个观察结果时，您的答案有何不同？

3.（12）当X1 = 4，X2 = 81和X3 = 43且置信水平为90％时，获得平均响应E {Y_h}的区间估计。指定点估计值，临界值和标准误差。

4.（12）当X1 = 4，X2 = 81和X3 = 43且置信度为90％时，获得单个响应Y _h {new}的间隔估计。指定点估计值，临界值和标准误差。

5.（14）当X1 = 4，X2 = 81和X3 = 43（置信水平为90％）时，获得具有相同预测值的两个预测的均值的区间估计。指定点估计值，临界值和标准误差。

6.（18）获得所有三个参数的Bonferroni同时置信区间，置信度为90％。

Then, fill in following blanks.

The p=__________, the critical value can be denoted by t(____, ____,____), and is computed as _____with R.

7. (24) Obtain a Working hoteling simultaneous confidence interval of the two mean responses where
Data point1: (X1=4, X2=81, X3=43);
Data point2: (X1=5, X2=70, X4=50)

with a 90% simultaneous confidence level (10).

Compare the method with the Bonferroni. Which method you prefer? (2)
How is your preference change under each of the following 3 cases? (12)
1). there are more and more data points to predict.
2). the sample size gets bigger.
3). the number of predictors gets bigger.