Q1) The regression run is

Dependent variable: log(output/plant)

Predictor                coef             squared error         

Constant                2.023           0.044 

Log(worker/plant)   0.745           0.081

Analysis of variance

Source                  DF               sum of squared

Regression             1                 1.062

Residual error        22                0.369

Total                     23               1.431

(1) coefficients of constant(b0), worker(b1), and plant(b2) ?

Output=b0 

b0 ?

b1 ?

b2 ?

(2) R-Sq. ?

(3) test H0: b1=0, H1: b1≠0, α=0.05 ?

(4) ) test H0: b1=0, H1: b1≠0, α=0.10, using F Distribution ?

Q2. The estimated regression equation is

Sales=12.7+140 North+96 Central+0.025 Income+0.017 NorthxIncome +0.006 CentralxIncome

R-sq=0.99, F=747.7, Base=South

(1) average sales in South, North, and Central ?

AS South ?

AS North ?

AS Central ?

(2) As South income increases $1, South sales change ?

As North income increases $1, North sales change ?

As Central income increases $1, Central sales change ?

Q3. The estimated regression equation is

Advertising=-43.8+0.019 Sales+0.479 Advertising(-1)

R-sq=0.96, F=233.4

(1) As sales in current year increases $1, Advertising change in next year ?

(2) As sales in current year increases $1, Advertising change in two year ?

Q4. The 5 students rate (1 ~ 10) on pizza A and pizza B:

Student        A       B

1                 6        8

2                 4        9

3                 5        4

4                 8        5

5                 3        7

(1) find Wilcoxon signed rank statistic T ?

(2) test H0: T=(ranksum(+) + ranksum(-))/2, α=0.05

H1: T<(ranksum(+) + ranksum(-))/2

Q5. The two-way analysis of variance table on fuel consumption(miles/gallon):

                   Source         DF      Sum of squared

K=3   car               2       6.16

H=5  driver           4        12.15

L=3   interaction    8        5.10

         Error            30      1.16

         Total            44      25.07           R-sq=0.96

(1) test H0: μ1=....= μk, H1: μ1≠....≠ μk, α=0.01

(2) test H0: μ1=....= μh, H1: μ1≠....≠ μh, α=0.01

(3) test H0: interaction Yes, H1: interaction No, α=0.01

Q5. The Laspeyres Price Index table:

Year             Food   Cloth  Meat

1 Quantity    140    420    110

1 Price          1.30   1.40   2.80

2 Price          1.40   1.10   3.00

3 Price          1.80   1.60   4.40

(1) Base year 1, LPI year 2 ?

                    LPI year 3 ?

(2) Base year changes to year 2, LPI year 1?

                                                 LPI year 2 ?

                                                 LPI year 3 ?

Q6. The quarterly earnings data:

Year.quarter  X

1.1               30

1.2               46

1.3               35

1.4               91

2.1               33

2.2               55

2.3               44

2.4               104

(1) 4-point moving averages for  1.2.1/2, ?

                                                 1.3/1/2 ?

1.4.1/2, ?

2.1.1/2 ?

2.2.1/2 ?

(2) central 4-point MA for 1.3 ?

                                      1.3 ?

                                      2.1 ?

                                      2.2 ?

(3) seasonal indexes for   1.3 ?

                                      1.4 ?

                                      2.1 ?

                                      2.2 ?

(4) seasonally adjusted earnings for  1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4 ?

Q7. The estimated auto regression model:

          Sales=314+1.18 Sales(-1)-0.36 Sales(-2)

          R-sq=0.77

(1) Sales(2013)=140 and Sales(2014)=130, Sales(2015) ?

(2) Sales(2016) ?