課程名稱︰統計學
課程性質︰系必修
課程教師︰雷立芬
開課學院：管院
開課系所︰國企系
考試日期（年月日）︰ 2010/6/23
考試時限（分鐘）： 2小時
是否需發放獎勵金： 是
（如未明確表示，則不予發放）
試題 :
1. Professor X, wanted to develop a multiple regression model to predict the
students' grades in his advanced statistics course for seniors. He dicided that
the tow most important factors are the students' grade point in the first three
years and the students' major. He proposed the model
Y=β+βX +βX +βX +ε
0 1 1 2 2 3 3
where
Y=advanced statistics course mark(out of 100)
X1=G.P.A in the first three years (range 0 to 12)
X2=1 if student's major is accounting, 0 if not
X3=1 if student's major is finance, 0 if not
The computer output (based on 100 students) appears below. However, because of
a printer malfunction, some of the results are not shown. These indicated by
the letter a to i.
Coefficients Standard Error t-Statistics
intercept a 7.10 1.29
X1 6.73 1.93 3.49
X2 10.42 b 2.50
X3 5.16 3.93 c
2
S = d R = e
yx
ANOVA
SOURCE df SS
REGRESSION f i
ERROR g 21553
TOTAL h 38651
a. Fill in the missing result. Show your calculation.(12pt)
b. Is there enough evidence at the 5% of significance level to conclude that
the model is useful in predicting the student's grades in fouth-year statistics
course? (10pt) 2 _2
c. What's the meaning of R ? Calculate R (5pt)
d. Predict the grade for a student who is a accounting major with GPA=3.5 (5pt)
2. Using a series of 25 annual observations, a student estimated the follow
regression model:
Yt=-509+0.89Xt1+17.27Xt2-21.20Xt3-0.522Xt4+7.36Xt5
(23.4) (3.24) (53.46) (0.175) (5.69)
where
Y=yearly Dow Jones Industrial Average;
Xt1= ratio of annual corporate profit to annual corporate sales;
Xt2= index of industrial production;
Xt3= Corporate bond yield;
Xt4= disposable income per capita;
Xt5= Consumer price index.
The figure in parentheses below the estimated coefficients are the estimated
_2
standard errors, R = 0.885, DW=1.046/
a. discuss the sign and statistical significance of each estimated coefficient.
b. Explain the meaning of Durbin-Watson tests(DW) in detail. Perform the test.
3. The manufacture of a nationally distributed brand of potato chips would like
to determine the feasibility of changing the product package from a cellphone
bag to an unbreakable container. The product manager believes that there would
be three possible national market response to a change in product packaging:
weak, moderate and strong. the projected payoffs, in increased or decreased
profit as compared with the current packaging, are as follow:
strategy
Event Use New Package Keep Old Package
Weak national response -$4,000,000 0
Moderate $3,000,000 0
Strong $5,000,000 0
On the basis of past experience, the product manager assigns the following
probabilities to the diffrent levels of national response:
P(weak)=0.30;P(moderate)=0.60;P(strong)=0.10
a. Set up the opportunity loss table.
b. Compute the expected monetary value for offering this new product package.
c. Compute the expected opportunity loss for offering this new product package.
d. Compute the expected value of perfect information and explain it.
e. On the basis of the results of (b) or (c), should the company offer this new
product package? Why?
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※ 編輯: ymwu 來自: 140.112.252.33 (06/28 00:12)