Stats413 Homework 11

Due Date: Apr 28, 6pm.
Answer all questions. Show all work.

E（书中的页面| X）= -0 + -1（出版世纪）+ -2中文+ -3其他

Q121.7R Q14.2≠6.6
1 c12.0d ˆ c 4.6 3.6≠3.1d — = a≠16.8b，V ar（-| X）= a 7.9≠3.6b

2.1 5.7 R 39.4 9.2

a）出版的世纪和书籍的长度之间是否有关系？

b）中文书籍的平均阅读长度比英文书籍平均吗？

c）中文书籍的平均长度是否比“其他”书籍的长度长？

d）为中文和英文书籍之间的平均长度差异提供估计的95％置信区间。

1个

b）证明se（-ˆ0 | K）= se（-ˆ0 + -ˆ1 | K）= se（-ˆ0 + -ˆ2 | K）。

（您只需执行这些推导操​​作即可显示出相等性，而无需得出最终值。提示：您需要开始对矩阵求逆，但是您可能不需要完成求逆。有3×3矩阵逆的封闭形式解决方案。）

2个

Stats413家庭作业11 R组件

1）通过查看离群值来检验此假设。您是否观察到任何县都可以提供这一假设的证据？如果是这样，请确定县。

2）检查变量，选择适当的转换并重新检查

Question 1

Consider a data set from a factory that produces widgets. The factor has 20 dierent fabricating machines, and each machine has 4 dierent workers on dierent shifts. Over the course of a shift, 10 widgets are randomly selected and measured for ecacy (measured in terms of percentage; 100% is full ecacy and 0% is inoperative.)

The main goal is to assess whether performance degrades or improves over time; performance of a given shift (do workers gets more tired?), performance over a workers career (do workers improve or do they get bored and lazy?), and performance over the lifetime of a machine (as the machine is used is it’s output quality decreased?)

On Canvas, take a look at the data set, hw10q1data.csv. (You can open it in R using read.csv(“hw11q1data.csv”, header = TRUE), or just in Excel.) This is a sample of the just two machines from the data.

You are tasked with fitting a model predicting ecacy based upon the three measures of time. Write down the expression for the observed value of ecacy. Include proper indices (and identify what each index represents). Do not forget the error structure.

Question 2

You ask a friend of yours to run the following model on 324 books:
E(pages in book|X) = 0 + 1(century of publication) + 2chinese + 3other

where “pages in book” is the number of pages, “century of publication” can take on {16, 17, 18, 19, 20, 21}, and “chinese” and “other” are dummy variables for the language of the book (reference = english).

Your friend, not having taken this class, provides you only with the following:

Q121.7R Q14.2 6.6
ˆ c12.0d ˆ ˆ c 4.6 3.6 3.1d = a16.8b , V ar(|X) = a 7.9 3.6b

2.1 5.7 R 39.4 9.2

Your stubborn “friend” now refuses to provide any other results. From this output, answer the following:

1. a)  Is there a relationship between century of publication and length of books?
2. b)  Are chinese books dierent length on average than english books?
3. c)  Are chinese books dierent length on average that “other” books?
4. d)  Provide an estimated 95% confidence interval for the average dierence in length between chinese and english books.

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