2008 First Semester STATS课程官方问答贴

z-score

阿童木会在奥大板块长期提供STATS课程的免费问答。本贴为大家提供assignment, course book, test & exam questions的帮助。

阿童木可以帮助的统计课程:

10x (4楼)
125 (5楼)
20x (6楼)
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为了方便大家，阿童木把不同课程的宝贵学习资料放到它们对应的帖子里。

本贴宗旨:

为人民服务，推广全民统计普及。

注意:

请大家在问问题前看一下2楼的贴规。

后缀:

想直接得到assignment答案的人们可以去assistance room或lab找为了省事直接给学生答案的tutor们，阿童木在这里会帮助想真正理解统计的朋友们去思考，得到最后的答案。

[ 本帖最后由 z-score 于 2008-3-28 12:15 编辑 ]

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• 4楼至13楼是不同papers的回复总结，求助问题前请check相关的楼，这样可以避免重复问题。
• 在每次跟帖的时候，请在标题中注明是哪门课程，例如：STATS210
  
• 请注明问题是哪一张paper的，本贴面向数多统计papers。
• 请适当给lz加人气
  

谢谢大家的合作

阿童木祝各位朋友在本学期的统计课程中得到满意的成绩。


[ 本帖最后由 z-score 于 2008-3-14 14:35 编辑 ]

z-score

这里的问题都是我在Summer School问答贴回答过的

为了阅读的方便，问题标为蓝色，回答标为红色。

20x General Questions

odds ratio是不是只需要知道怎麽寫executive summary?

是的，因为odds ratio的technical notes就是R code.

1e-3=0.001?

是的。

20x Tutorial Questions

Tutorial 10 ADD data:

"The plot of Cook’s distance shows none of the observations have an undue influence
on the final model. Observation 78 has a large value of Cook’s distance, relative to the
other observations, but removing it did not change any of the coefficients by more
than a standard error, so it was retained."

是怎么看删去unusual observations后，有没有SIGNIFICANT CHANGE呀？
还有。所说的“did not change any of the coefficients by more than a standard error”是怎么看出来的？

new coefficient - old coefficient
- -！是全部的VARIABLE都要试过去吗？
你能拿这个例子示范一下怎么算给我看吗？谢谢。

> exam.fit3<-lm(Exam~Assign+Test+I(Test^2)+Stage1,
data=course.df[-106,])
> summary(exam.fit3)
Coefficients:
                    Estimate   Std. Error t value Pr(>|t|)
(Intercept)     31.42284 6.37936    4.926  2.35e-06 ***
Assign          1.35513 0.24074 5.629 9.65e-08 ***
Test             -0.83163 1.11701 -0.745 0.45782
I(Test^2)      0.12584 0.04633 2.716 0.00745 **
Stage1B       -5.22603 2.19378 -2.382 0.01856 *
Stage1C       -12.78126 2.34233 -5.457 2.16e-07 ***

> summary(exam.fit2)
                 Estimate   Std. Error t value Pr(>|t|)
(Intercept)  30.69567 6.49900    4.723 5.58e-06 ***
Assign        1.56651   0.23068    6.791 2.93e-10 ***
Test           -1.24720 1.12706     -1.107 0.27036
I(Test^2)    0.13846   0.04698    2.947 0.00376 **
Stage1B     -4.45745  2.21620    -2.011 0.04621 *
Stage1C     -11.84911 2.35973   -5.021 1.54e-06 ***

IF((new coefficient - old coefficient)/old standard error)>1
THEN influential

除了intercept

Assign (1.56651-1.35513)/0.24074=?

下面的test, test2, stage1B和stage1C都要试，如果很多都是>1, 106就是influential.

还有。。。我刚才看CASE STUDY ：PERUVIAN INDIANS。。
((new coefficient - old coefficient)/old standard error) 如果是-1 -2什么的是不是也算？
因为我算了下 weight是(0.82103-1.263)/0.31261=-1.4139

嗯，是的，是绝对值。

Tutorial 11: Logistic Regression & Time Series
Meningitis Data那道题。。。

Using the output from the seasonal factor model (page 506), calculate the forecast of
the log of the number of notified cases of meningitis for January 1998.

The seasonal factor log model is:
log.meningitist = 0.628026 + 0.019481 × time – 0.252158 × month2 + … +
0.064355 × month12 + 0.321058 × log.meningitist-1

We are forecasting for January 1998 i.e. time period 97
log.meningitis97 = 0.628026 + 0.019481 × 97 – 0.252158 × 0 + … +
0.064355 × 0 + 0.321058 × log.meningitis96

= 0.628026 + 0.019481 × 97 – 0.252158 × 0 + … +
0.064355 × 0 + 0.321058 × 3.988984
= 3.798378225

我想知道。。。log.meningitis96也就是 3.988984是怎么得出来的？

不是题目里面的54吗？你log(64)=3.988984

20x Past Exam Questions

PAST EXAM PAPER....2007 S2....SECTION A.......
QUESTION 7&10...怎麽算答案都不對....阿童木能演算一下嗎?謝謝...

Question 10

> exp(log((35*155)/(129*11))-1.96*sqrt(1/35+1/11+1/129+1/155))
[1] 1.867189

Answer is the first 1.

Question 7

> exp(2.797203+0.010852*85+0.509277*log(104660))
[1] 14854.93

Answer is the fourth 1.

我想問一下....2007 S1
question 3 為什麽選項3是錯的?
question 7 為什麽選項2是錯的?還有第3個和第5個選項是怎麽算出來的...
question 14 爲什麽選項1是錯的?

謝謝

2007S1
Question 3

(3)We estimate that the odds of dying for a patient admitted to ICU withan infection are about 0.77 times the odds for a patient admittedwithout an infection.

Coefficients:
        Estimate Std. Error z value Pr(>|z|)
INF  0.76525  0.41681   1.836   0.066360 .

> exp(0.76525)
[1] 2.149532

得到odds需要back-transform. 0.77没有transform.

Question 7

Coefficients:
             Estimate     Std. Error  t value    Pr(>|t|)
time[-1] 1.194e-02   1.792e-03  6.664      9.77e-11 ***

2) For each additional unit of time, the CO2 concentration increases by about 0.012 ppm, on average.

这句是错的因为不是the CO2 concentration increases by about 0.012, 是the mean CO2 concentration increases by about 0.012.

(3) We estimate that the autocorrelation coefficent (rho) is about 0.78

Coefficients:
                         Estimate     Std. Error  t value    Pr(>|t|)
dioxide.ts[-384]   7.777e-01  3.289e-02  23.648    < 2e-16 ***

7.777e-01, 这个是estimated rho.

(5) A point estimate for the difference in average CO2 concentrationbetween July and August of each year is about 0.887 ppm, having allowedfor the trend and for autocorrelation.

Coefficients:
                         Estimate     Std. Error  t value    Pr(>|t|)
month[-1]7        -1.636e+00 1.273e-01  -12.846 < 2e-16 ***
month[-1]8        -2.523e+00 9.083e-02  -27.782 < 2e-16 ***

> -2.523--1.636
[1] -0.887

Question 14

(1) A high value for R2 indicates that our model will be useful for prediction.

A regression model will only be useful for prediction if and only ifthe R2 is high and having satisfied the normality assumption.

2007 SS
question 9
option 1是怎麽算出來的?
option 5為什麽是錯的?

2007SS Question 9

(1) Using the regression model, our point prediction for the 1st quarter 2003 is about 15.4 million litres.
> beer.pred
                fit             upr           lwr
2003 Q1 15224.24 19383.60 11064.886

15224大约等于15.4million.

(5) The point prediction for the 4th quarter of 2004, using theregression model does not lie within the prediction interval weobtained using the Holt-Winters technique.

在Holt-winters, point estimate是C.I.的中间值。所以does not lie within是错的。

thanks...

For 2006 Second semester ...
question 10. how to get the answers for option 4 and 5?

2006SC Question 10

> predictions
                fit               upr             lwr
Jan 1973 0.3860656 0.7937101 -0.021578940

(4) Our point prediction for ozone concentration for January 1973 is about 1.47 ppm.

(5) We estimate ozone concentration for January 1973 will be between 0.98 ppm and
2.21 ppm.

> exp(c(0.3860656,0.7937101,-0.021578940))
[1] 1.4711812 2.2115864 0.9786522

For first semester 2006
question 5
the option 2
why we cannot qualify the difference in average ages using this analysis?

That's because the analysis was done on the transformed data.

summer school 2006
question 18 b) 爲什麽是用chi-square test...hourly attendance不是quantitative variable嗎?

因为这是一个trick, hourly attendance你就record(count)一次，所以你没有quantiative variable, it's not a variable, it's only a count.

2007 S2
Q9 option 4 是怎么算的？谢谢

2007SC Question 9

(4) We estimate that if a patient required resuscitation, the odds of survival are
multiplied by about 0.2

Coefficients:
              Estimate Std. Error z value Pr(>|z|)
CPR     -1.63066 0.61553   -2.649  0.00807 **

> exp(-1.63066)
[1] 0.1958003

我又来了~

想问一下..2006 SUMMER SCHOOL的QUESTION 8
为什么第一个选项是对的...第二个是错的?

2006 SS
Question 8

(1) The residuals appear to be reasonably symmetric.

Residuals:
Min           1Q             Median     3Q           Max
-0.060829 -0.013325 0.002093 0.012705 0.047020

5 number summary shows the residuals appear to be symmetric.

(2) The t-statistic for testing the hypothesis that there is no trend is about 6 million litres.

Coefficients:
                 Estimate     Std. Error   t value Pr(>|t|)
time[-1]    0.0016375 0.0002039 ***** 2.43e-13 ***

t = > 0.0016375/ 0.0002039
[1] 8.030897

2007 SS
question 10:
爲什麽第一個選項是對的,第二個選項是錯的?

還有就是question 18不是會讓我們選擇which form of analysis should be used to investigate嗎?
在什麽情況下  我們會用到logistic regression?

2007SS

(1)The confidence interval for the odds of dying for patients admitted ina semiconscious state compared to the odds of dying for patientsadmitted in a conscious state will contain 1
Coefficients:
            Estimate   Std. Error    z value Pr(>|z|)
LOC1   18.60221 1039.99658 0.018  0.985729

The P-value 0.985729 refers to the hypothesis that the log oddsassociated with LOC1 is zero. After backtransforming, exp(0) = 1, sothe confidence interval should contain 1 as an insiginificant P-valuecontains the hypothesised value.

(2) For each additional year of age of patients admitted to ICU, the odds of dying increase by about 0.03

Coefficients:
         Estimate Std. Error z value Pr(>|z|)
AGE  0.03072 0.01268   2.423  0.015377 *

The log odds increases by about 0.03, not the odds.

For question 18, you use logistic regression when your response variable is qualitative binary variable.

[ 本帖最后由 z-score 于 2008-2-28 21:11 编辑 ]

z-score

学习资料附件的解释:

STATS10x Worked Examples - 阿童木的例题工作过程

[ 本帖最后由 z-score 于 2008-9-11 21:32 编辑 ]

z-score

学习资料附件的解释:

[ 本帖最后由 z-score 于 2008-9-11 21:32 编辑 ]

z-score

学习资料附件的解释:

STATS20x.zip - 本学期所有的assignment数据

STATS20x Worked Examples - 阿童木的例题工作过程

[ 本帖最后由 z-score 于 2008-9-11 21:34 编辑 ]

z-score

更新中

[ 本帖最后由 z-score 于 2008-3-14 11:31 编辑 ]

z-score

更新中

[ 本帖最后由 z-score 于 2008-2-28 20:12 编辑 ]

z-score

更新中

Study 3: A road safety researcher was interested in the effects ofalcohol on the driving ability of young adults. A sample of 50 youngadults was obtained and each was randomly allocated to either analcohol group or a no alcohol group. The members of the alcohol groupeach drank 700ml of beer then did a 10 minute session on a drivingsimulator. The members of the no alcohol group just did a 10 minutesession on a driving simulator. For each member, the driving simulatorreported the number of errors made during their 10 minute session.

(d) For study 3, students had differing drinking histories, with somebeing heavy drinkers, some being moderate drinkers and some being milddrinkers.
Consider the statement: “The two groups of students in study 3__________ roughly balanced with respect to previous drinking history.”
Which one of the following phrases would best fill in the missing gap in the statement?
“will be” “are likely to be” “are not likely to be” “wont be”
Briefly justify your choice.

他都没有说作出来结果是怎样，要怎么决定？他是不是
ballance

帮帮我吧

嗯，这个问题问得很好。你考虑问题里的这点:

Study 3: A road safety researcher was interested in the effects ofalcohol on the driving ability of young adults. A sample of 50 youngadults was obtained and each was randomly allocatedto either an alcohol group or a no alcohol group. The members of thealcohol group each drank 700ml of beer then did a 10 minute session ona driving simulator. The members of the no alcohol group just did a 10minute session on a driving simulator. For each member, the drivingsimulator reported the number of errors made during their 10 minutesession.

为什么我们要randomly allocate？

因为我们知道所有的驾驶者能分为三种，他们承受酒精的能力不同，这会影响最重的结果。randomallocation方法 wishes to achieve a fair and balanced comparison betweendifferent groups. 意思是说，随即的取样可以试图得到balanced samples。

如果我们再考虑一下，在统计里，我们能有will be吗？（能有绝对性吗？) 同样，我们能有won't be吗？（绝对不可能）

所以答案应该是？


SELF-SELECTION BIAS。AND THE SELECTION BIAS。。好像大同小异。。我看概念了。。。 可真正区分要犹豫好久。。才能判断出。。  请你讲解下哦 。。 谢谢。。。

Selection bias和self selection bias的最大区别是selection bias是在一个sample里出现，self selection没有一个固定的sample。

Selection bias指的是你的sample与population of interest不一样。

Self selection bias指的是当你没有一个固定的sample下，那些自愿参加调查人所带来的偏差。


我有一个问题啊:
1.observation studies 和 experiments有什么不同? 请分别给解释一下 谢谢



Experiments可以randomly allocate subjects, 意思是说如果你从新再搞一次试验，在A组的人或东西可以变为B组的人或东西。每次试验，不同组的组合纯属依靠几率。

Observational study的不同组不能改变，举例子: 比较男女或老少。男就是男，不是我们randomly allocate给他的。如果老就是老，不是我们给他的年龄。

sampling error 和 non-sampling error的解释好象Course book上并没有明确指出 就麻烦LZ了! 谢谢

这是一个很好的问题。

你来想象一个飞镖与飞镖盘。

假设你扔了4个飞镖，你这4个飞镖的中心与飞镖盘的圆心的距离就是non-sampling error。

你这4个飞镖与这4个飞镖中心的距离就是sampling error。

[ 本帖最后由 z-score 于 2008-4-1 11:13 编辑 ]

萨米

我也留一个

萨米

我再留一个

apricotnz

感谢啊~~~~~~~~~~~

luvwei

Study 3: A road safety researcher was interested in the effects of alcohol on the driving ability of young adults. A sample of 50 young adults was obtained and each was randomly allocated to either an alcohol group or a no alcohol group. The members of the alcohol group each drank 700ml of beer then did a 10 minute session on a driving simulator. The members of the no alcohol group just did a 10 minute session on a driving simulator. For each member, the driving simulator reported the number of errors made during their 10 minute session.

(d) For study 3, students had differing drinking histories, with some being heavy drinkers, some being moderate drinkers and some being mild drinkers.
Consider the statement: “The two groups of students in study 3 __________ roughly balanced with respect to previous drinking history.”
Which one of the following phrases would best fill in the missing gap in the statement?
“will be” “are likely to be” “are not likely to be” “wont be”
Briefly justify your choice.

他都没有说作出来结果是怎样，要怎么决定？他是不是
ballance

帮帮我吧

当时的理想

我STAT108ASSIGMENT的第1题。。都看得头晕晕的。。。 要怎么算哦 ？？？

谢谢。。。     就是算COURSE WORK的那些东西。。。 很不理解。。

t-multiplier

原帖由 luvwei 于 2008-3-8 12:18 发表
Study 3: A road safety researcher was interested in the effects of alcohol on the driving ability of young adults. A sample of 50 young adults was obtained and each was randomly allocated to eith ...

For study 3, students had differing drinking histories, with some beingheavy drinkers, some being moderate drinkers and some being milddrinkers.
Consider the statement: “The two groups of students in study 3__________ roughly balanced with respect to previous drinking history.”
Which one of the following phrases would best fill in the missing gap in the statement?
“will be” “are likely to be” “are not likely to be” “wont be”
Briefly justify your choice.

嗯，这个问题问得很好。你考虑问题里的这点:

Study 3: A road safety researcher was interested in the effects of alcohol on the driving ability of young adults. A sample of 50 young adults was obtained and each was randomly allocated to either an alcohol group or a no alcohol group. The members of the alcohol group each drank 700ml of beer then did a 10 minute session on a driving simulator. The members of the no alcohol group just did a 10 minute session on a driving simulator. For each member, the driving simulator reported the number of errors made during their 10 minute session.

为什么我们要randomly allocate？

因为我们知道所有的驾驶者能分为三种，他们承受酒精的能力不同，这会影响最重的结果。random allocation方法 wishes to achieve a fair and balanced comparison between different groups. 意思是说，随即的取样可以试图得到balanced samples。

如果我们再考虑一下，在统计里，我们能有will be吗？（能有绝对性吗？) 同样，我们能有won't be吗？（绝对不可能）

所以答案应该是？


[ 本帖最后由 t-multiplier 于 2008-3-8 15:19 编辑 ]

t-multiplier

原帖由 当时的理想 于 2008-3-8 14:41 发表
我STAT108ASSIGMENT的第1题。。都看得头晕晕的。。。 要怎么算哦 ？？？

谢谢。。。     就是算COURSE WORK的那些东西。。。 很不理解。。

其实这个很简单，就是问你的多少分才可以pass. 你可以参考我在4楼的worked examples.

当时的理想

你的WORK EXAMPLE。。 下载了。。打开为什么是空白的 ？？

当时的理想

为什么打不开你的呢？

还有。。想问 。。ASSIGMENT是怎么计算分数的 ？？  以前高中是你拿到几个A1什么的就可以拿到全部分数。。。  这个ASSIG有40分。。几分及格哦？  是不是像NCEA。。 你答对1半就可以拿到全部分数。。然后分 C .. B..B+那样的呢？？

谢谢 。。

第一题。。我真的不懂怎么算。。。答案是45%？？  第2 小题不知道要怎么EXPLAIN。。。

当时的理想

SELF-SELECTION BIAS。AND THE SELECTION BIAS。。好像大同小异。。我看概念了。。。 可真正区分要犹豫好久。。才能判断出。。  请你讲解下哦 。。 谢谢。。。

z-score

原帖由 当时的理想 于 2008-3-8 17:09 发表
你的WORK EXAMPLE。。 下载了。。打开为什么是空白的 ？？

啊？不会吧。我刚才还试了一下，你的电脑有Adobe Reader吧？那个文件是pdf file.

z-score

原帖由 当时的理想 于 2008-3-8 20:26 发表
为什么打不开你的呢？

还有。。想问 。。ASSIGMENT是怎么计算分数的 ？？  以前高中是你拿到几个A1什么的就可以拿到全部分数。。。  这个ASSIG有40分。。几分及格哦？  是不是像NCEA。。 你答对1半就可以拿到 ...

奥大的课程和NCEA课程计算分数方法不一样。Assignment的分数会是0到10中间的一个整数。如果你得到37/40，你会被提升到10（满分），如果你得到21/40，你会被提升到6。

第二题他在问你这门课的最终成绩可以怎样计算。你需要把两种不同计算方法都写出来。你明白我说的意思吗？

z-score

原帖由 当时的理想 于 2008-3-8 20:28 发表
SELF-SELECTION BIAS。AND THE SELECTION BIAS。。好像大同小异。。我看概念了。。。 可真正区分要犹豫好久。。才能判断出。。  请你讲解下哦 。。 谢谢。。。

Selection bias和self selection bias的最大区别是selection bias是在一个sample里出现，self selection没有一个固定的sample。

Selection bias指的是你的sample与population of interest不一样。

Self selection bias指的是当你没有一个固定的sample下，那些自愿参加调查人所带来的偏差。

ysm860929

新生好可爱,这些分怎么算,以后Assignment做多了就知道了

阴雨天

我有一个问题啊:
1.observation studies 和 experiments有什么不同? 请分别给解释一下 谢谢

阴雨天

还有一个问题111
A group of biologists is interested in surveying the abundance of barrel cactus in a particular desert. They divide the desert area up into 1200 equal sized rectangular areas. Of these, 247 areas are too difficult to access, so are excluded. Of the remaining 953 areas, 50 are chosen at random to be surveyed. The biologists then randomly select a 100 square metre section of each of these areas to survey. The number of barrel cacti in each of the chosen sections is then measured.
Briefly describe how you could use a table of random numbers to select 50 out of the 953 areas to survey.

非常感谢!!!

阴雨天

sampling error 和 non-sampling error的解释好象Course book上并没有明确指出 就麻烦LZ了! 谢谢

luvwei

谢谢搂住啊

z-score

原帖由 阴雨天 于 2008-3-9 13:10 发表
我有一个问题啊:
1.observation studies 和 experiments有什么不同? 请分别给解释一下 谢谢

阿童木现在还没有回家，过一会儿回到家我马上给你解答。

回来了，哦耶。

Experiments可以randomly allocate subjects, 意思是说如果你从新再搞一次试验，在A组的人或东西可以变为B组的人或东西。每次试验，不同组的组合纯属依靠几率。

Observational study的不同组不能改变，举例子: 比较男女或老少。男就是男，不是我们randomly allocate给他的。如果老就是老，不是我们给他的年龄。

[ 本帖最后由 z-score 于 2008-3-9 19:26 编辑 ]

z-score

原帖由 阴雨天 于 2008-3-9 13:15 发表
还有一个问题111
A group of biologists is interested in surveying the abundance of barrel cactus in a particular desert. They divide the desert area up into 1200 equal sized rectangular areas. Of ...

你会用course book后面的那个table of random numbers吗？这个问题就是让你解释你能怎样用table of random numbers。

[ 本帖最后由 z-score 于 2008-3-9 19:34 编辑 ]

z-score

原帖由 阴雨天 于 2008-3-9 13:50 发表
sampling error 和 non-sampling error的解释好象Course book上并没有明确指出 就麻烦LZ了! 谢谢

这是一个很好的问题。

你来想象一个飞镖与飞镖盘。

假设你扔了4个飞镖，你这4个飞镖的中心与飞镖盘的圆心的距离就是non-sampling error。

你这4个飞镖与这4个飞镖中心的距离就是sampling error。