
A
Interpretation: Construct a regression formula for anticipating the overhead expense using linear regression, based on the project duration.
Concept Introduction: The method followed in predicting the future value depending on the previous forecast including the portion of errors in the previous forecast is called Simple Exponential Smoothing forecast.
A

Answer to Problem 32P
The required regression equation for predicting overhead expense is Y=5399.22+29.7217x.
Explanation of Solution
Given Information:
Project Code | Project Duration (days) (X) | Overhead Expense (Y) | XY | X2 |
A11 | 72 | $5,900 | $424,800 | 5184 |
A12 | 158 | $10,303 | $1,627,874 | 24964 |
A14 | 124 | $9,054 | $1,122,696 | 15376 |
A18 | 96 | $6,644 | $637,824 | 9216 |
A22 | 152 | $10,718 | $1,629,136 | 23104 |
B2 | 174 | $10,332 | $1,797,768 | 30276 |
B33 | 124 | $8,804 | $1,091,696 | 15376 |
B23 | 105 | $8,884 | $932,820 | 11025 |
B10 | 63 | $7,916 | $498,708 | 3969 |
B14 | 58 | $8,267 | $479,486 | 3364 |
B7 | 83 | $8,503 | $705,749 | 6889 |
109.9090909 | 8665.9091 | 10948557 | 148743 | |
12080.00826 | ||||
b | 29.7217 | |||
a | 5399.22 |
Thus, the regression equation with the derived values will be,
B
Interpretation: Find out the coefficient of determination for the given projects.
Concept Introduction: The proportion of variance occurring in the dependent variable forecasted based on the independent variable is called the Coefficient of Determination.
B

Answer to Problem 32P
The coefficient of determination, r2 is 0.6264.
Explanation of Solution
Given Information:
Project Code | Project Duration (days) (X) | Overhead Expense (Y) |
A11 | 72 | $5,900 |
A12 | 158 | $10,303 |
A14 | 124 | $9,054 |
A18 | 96 | $6,644 |
A22 | 152 | $10,718 |
B2 | 174 | $10,332 |
B33 | 124 | $8,804 |
B23 | 105 | $8,884 |
B10 | 63 | $7,916 |
B14 | 58 | $8,267 |
B7 | 83 | $8,503 |
r2 | 0.6264 |
Thus, coefficient of determination is 0.6264.
C
Interpretation: Determine what the forecast of the overhead expense suggests for the project of 110 days long.
Concept Introduction: Using regression, we will be able to define relationship between any two variables, denoting the cause and effect. The method can also be used to forecast the future depending on the past performances.
C

Answer to Problem 32P
The forecasted expense of overhead for 110 days long project is $8,668.61.
Explanation of Solution
Given Information:
The project is 110 days long.
Thus, the forecasted overhead expense is $8,668.61.
D
Interpretation: With the information, build a better way in using linear regression for
Concept Introduction: Using regression, we will be able to define relationship between any two variables, denoting the cause and effect. The method can also be used to forecast the future depending on the past performances.
D

Answer to Problem 32P
The forecasted overhead expense is $8946.64.
Explanation of Solution
Given Information:
The given value of ‘a’ is 1542.02 and the given value of ‘b’ is 57.99.
Project Code | Project Duration (days) (X) | Overhead Expense (Y) | XY | X2 |
A11 | 72 | $5,900 | $424,800 | 5184 |
A12 | 158 | $10,303 | $1,627,874 | 24964 |
A14 | 124 | $9,054 | $1,122,696 | 15376 |
A18 | 96 | $6,644 | $637,824 | 9216 |
A22 | 152 | $10,718 | $1,629,136 | 23104 |
120.4 | $8,524 | 5442330 | 77844 | |
14496.2 | ||||
b | 57.99 | |||
a | 1542.02 | |||
r2 | 0.9655 |
Thus, with the above derived values of ‘a’ and ‘b’, the linear regression model would be:
Now, substituting the values in the previous linear regression equation:
For 110 days, the forecasted overhead expense is $7920.92.
Now, substituting the values in the later linear regression equation:
Thus, the forecasted overhead expense is $8946.64.
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Chapter 4 Solutions
Practical Operations Management
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