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) ?