The president of a small manufacturing firm is concerned about the continual inc
ID: 2931645 • Letter: T
Question
The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per unit for the firm's leading product over the past eight years.
Click on the datafile logo to reference the data.
Year
Cost/Unit ($)
Year
Cost/Unit ($)
1
20.00
5
26.60
2
24.50
6
30.00
3
28.20
7
31.00
4
27.50
8
36.00
Year
Cost/Unit ($)
1
20.0
2
24.5
3
28.2
4
27.5
5
26.6
6
30.0
7
31.0
8
36.0
B) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
MSE=
(c)
What is the average cost increase that the firm has been realizing per year?
Round your interim computations and final answer to two decimal places.
$
Year
Cost/Unit ($)
Year
Cost/Unit ($)
1
20.00
5
26.60
2
24.50
6
30.00
3
28.20
7
31.00
4
27.50
8
36.00
Explanation / Answer
B) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
Solution:
First of all we have to find the regression equation for the estimation of the cost per unit in $. The regression output by using excel is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.92187792
R Square
0.849858899
Adjusted R Square
0.824835382
Standard Error
1.972569833
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
132.1488095
132.1488
33.96241
0.001123212
Residual
6
23.34619048
3.891032
Total
7
155.495
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
19.99285714
1.537014031
13.0076
1.27E-05
16.2319193
23.75379498
Year
1.773809524
0.304374133
5.827728
0.001123
1.029032851
2.518586196
From the above regression analysis, the regression equation is given as below:
Cost/Unit ($) = 19.9929 + 1.7738*Year
For X=1, Cost/Unit ($) = 19.9929 + 1.7738*1 = 21.7667
For X=2, Cost/Unit ($) = 19.9929 + 1.7738*2 = 23.5405
.
.
Estimated values of Y and squared errors are summarised as below:
Year (X)
Cost/Unit ($) (Y)
Estimated cost/unit ($)(Y)
Error
Squared error
1
20
21.7667
-1.767
3.121229
2
24.5
23.5405
0.9595
0.92064
3
28.2
25.3143
2.8857
8.327264
4
27.5
27.0881
0.4119
0.169662
5
26.6
28.8619
-2.262
5.116192
6
30
30.6357
-0.636
0.404114
7
31
32.4095
-1.41
1.98669
8
36
34.1833
1.8167
3.300399
Total
23.34619
Mean squared error = squared error/n = 23.34619/8 = 2.91827375
MSE = 2.91827375
(c) What is the average cost increase that the firm has been realizing per year?
Solution:
The regression equation for estimation of dependent variable or response variable cost/unit ($)(Y) is given as below:
Cost/Unit ($) = 19.9929 + 1.7738*Year
For the above regression equation, the slope is given as $1.7738 which indicates the average cost increase that the firm has been realizing per year.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.92187792
R Square
0.849858899
Adjusted R Square
0.824835382
Standard Error
1.972569833
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
132.1488095
132.1488
33.96241
0.001123212
Residual
6
23.34619048
3.891032
Total
7
155.495
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
19.99285714
1.537014031
13.0076
1.27E-05
16.2319193
23.75379498
Year
1.773809524
0.304374133
5.827728
0.001123
1.029032851
2.518586196
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