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A regression equation covering electricity costs high-cost month and the low-cost month. If costs were $400 in April when production was 800 machine hours and $600 in September when production was 1,300 hours
:High month $600 for 1,300 hours
:Low month 400 for 800 hours:
Increase $200 500 hours
Because costs increased $200 for 500 additional hours, the variable cost is $.40 per machine hour. For the low month, the total variable portion of that monthly cost is $320 ($.40 x 800 hours). Given that the total cost is $400 and $320 is variable, the remaining $80 must be a fixed cost. The regression equation is y = 80 + .4x.
Learning curve analysis
An 80% learning curve indicates that a doubling of production will reduce average unit completion time by 20%. 16 units what will be cumulative avg time per unit starts with 100 minutes
2 80 (100 x 80%)
4 64 (80 x 80%)
8 51.2 (64 x 80%)
16 40.96 (51.20 x 80%)
a) the average of the units in the fifth batch alone must have been 30.72 minutes [(40.96 minutes x 2) —
Two methods of applying learning curve analysis are in common use:
-The cumulative average-time learning model projects the reduction in the cumulative average time it takes to complete a certain number of tasks.
-The incremental unit-time learning model projects the reduction in the incremental time it takes to complete the last task.
Time series analysis ?
Time series analysis is the process of projecting future trends based on past experience (for this reason, it is also called trend analysis). It is a regression model in which the independent variable is time.
Time series/trend analysis encompasses three main techniques:
1.Simple Moving Average
2.Weighted Moving Average
Simple Moving Average
1) The data points are summed and divided by the number of time periods. This process is repeated for successive groups of time periods.
2) Thus, the average includes each new observation and discards the oldest observation.
. Weighted Moving Average
This technique allows a firm to give each data point a weight indicating its relative importance in determining the outcome.
a. Exponential smoothing is a forecasting technique used to level or smooth variations encountered in a forecast. It also adapts the forecast to changes as they occur.
The expected value of an event is calculated by multiplying the probability of each outcome by its payoff and summing the products.
SN 1 No road is ever built. .1
SN 2 A road is built this year. .2
SN 3 A road builtthan 1 year from now.7
Bivens Tract$10,000 $40,000 $35,000
Bivens tract .1(10k) +2.(40k) +.7(35k) = 33,500
In regression analysis, which of the following coefficients of correlation represents the
strongest relationship between the independent and dependent variables?
Answer (C) is correct. Because the range of values is between -1.0 and 1.0, -.89 suggests a
very strong inverse relationship between the independent and dependent variables. A value of
-1.0 signifies a perfect inverse relationship, and a value of 1.0 signifies a perfect direct
The manager of the assembly department of a company would like to estimate the fixed and
variable components of the department's cost. To do so, the manager has collected information
on total cost and output for the past 24 months. To estimate the fixed and variable components
of total cost, the manager should use
Answer (A) is correct. Regression analysis is a statistical technique for measuring the
relationship between variables. It estimates the component of the dependent variable that
varies with changes in the independent variable and the component that does not vary.
A regression equation
A. Estimates the dependent variables.
B. Encompasses factors outside the relevant range.
C. Is based on objective and constraint functions.
D. Estimates the independent variable.
Answer (A) is correct. Regression analysis is used to find an equation for the linear
relationship among variables. The behavior of the dependent variable is explained in terms of
one or more independent variables. Regression analysis is often used to estimate a dependent
variable (such as cost) given a known independent variable (such as production).
In the standard regression equation y = a + bx, the letter b is best described as a(n)
Answer (D) is correct. In the standard regression equation, b represents the slope of the
regression line. For example, in a cost determination regression, y equals total costs, b is
the variable cost per unit, x is the number of units produced, and a is fixed cost.
The letter x in the standard regression equation is best described as a(n)
Answer (A) is correct. The letter x in the standard regression equation is the independent
variable. For example, in a regression to determine the total cost of production, x equals
In a multiple regression analyses there are three components
1. Fixed cost
2. Dependent variable 1
3. Dependent variable 2
A change to what would invalidate this equation the most?
In multiple regression, a large difference between the expected
value and the actual value of one of the coefficients has the most impact in rendering the
model invalid. A change in costs would be incorporated into the equation automatically,
but a change in productivity per hour would not.
The least exact method for separating fixed and variable costs is
A. The least squares method.
B. Computer simulation.
C. The high-low method.
D. Matrix algebra.
Answer (C) is correct. The fixed and variable portions of mixed costs may be estimated by
identifying the highest and the lowest costs within the relevant range. The difference in cost
divided by the difference in activity is the variable rate. Once the variable rate is found, the
fixed portion is determinable. The high-low method is a simple approximation of the mixed
cost formula. The costs of using more sophisticated methods sometimes outweigh the
incremental accuracy achieved. In these cases, the high-low method is sufficient
If there is a strong statistical relationship between the sales and customers' income levels,
which of the following numbers best represents the correlation coefficient for this relationship?
The coefficient of correlation measures the relative strength of the
linear relationship. The range of the coefficient (r) is -1.0 ≤ +1.0. The value of -1.0
indicates a perfectly inverse linear relationship between x and y (i.e., as x increases, y
decreases). A value of zero indicates no linear relationship between x and y. A value of
+1.0 indicates a perfectly direct relationship between x and y. Because Fairfield's sales
decrease as income levels increase, the inverse linear relationship is very strong. This
inverse relationship is best represented by -.93.
A computer generated two possible regression equations to use.
1. Machine hours
Y intercept =2,500
B = 5.0
2.DM weight, y intercept 4,600
The value of r² indicates the proportion of the total variation in y that is explained by the regression equation. Because machine hours has a higher r² than direct materials weight, the coefficients for machine hours are used to
predict costs. Consequently, the regression equation is y = 2,500 + 5.0x
Which of the following may be used to estimate how inventory warehouse costs are affected by
both the number of shipments and the weight of materials handled?
A. Economic order quantity analysis.
B. Probability analysis.
C. Correlation analysis.
D. Multiple regression analysis.
Answer (D) is correct. Multiple regression analysis involves the use of a linear equation.
This equation consists of one dependent variable and more than one independent variable.
Accordingly, estimating inventory warehouse costs involves both a dependent variable
and independent variables. Hence, multiple regression should be used to estimate these
Given demand in excess of capacity, no spoilage or waste, and full use of a constant number of
assembly hours, the number of components needed for an assembly operation with an 80%
learning curve should
I. successive periods.
II. Decrease per unit of output.
A. I only.
B. II only.
C. Both I and II.
D. Neither I nor II.
An 80% learning curve means that the cumulative average time
required to complete a unit (or the time required to produce the last unit) declines by 20%
when unit output doubles in the early stages of production. Thus, as the cumulative average
time per unit (or the time to complete the last unit) declines, the number of units produced per
period of time increases. As more units are produced, more components are needed for the
production. The number of components per unit of output is not affected by an increase in
Learning curves are best used to predict
A. Unit material costs.
B. Overhead variances.
C. Total unit costs.
D. Unit direct labor costs.
Answer (D) is correct. Learning curves reflect the increased rate at which people perform
tasks as they gain experience. Thus, they are useful in predicting unit direct labor costs.
A forecasting technique that is a combination of the last forecast and the last observed value is
B. Least squares.
D. Exponential smoothing
Answer (D) is correct. Exponential smoothing is a widespread technique for making
projections because it requires less data be kept on hand than the moving average methods. The
technique involves weighting the actual result for the previous period by a smoothing factor,
weighting the forecast for the previous period by the smoothing factor's complement, and
combining the two.
As part of a risk analysis, an auditor wishes to forecast the percentage growth in next month's
sales for a particular plant using the past 30 months' sales results. Significant changes in the
organization affecting sales volumes were made within the last 9 months. The most effective
analysis technique to use would be
Under exponential smoothing, each forecast equals the sum of the
last observation times the smoothing constant, plus the last forecast times one minus the
constant. Thus, exponential means that greater weight is placed on the most recent data,
with the weights of all data falling off exponentially as the data age. This feature is
important because of the organizational changes that affected sales volume.
What are the four components of a time series?
. 1. Trend
What is the Moving Average method of forecasting?
Includes each new observation in the average as it becomes available and discards the
The simple moving-average method is a smoothing technique that uses
the experience of the past N periods (through time period t) to forecast a value for the next
period. Thus, the average includes each new observation and discards the oldest observation.
The forecast formula for the next period (for time period t+1) is the sum of the last N
observations divided by N.
Which tool would most likely be used to determine the best course of action under conditions
Cost-volume-A. profit analysis.
B. Expected value (EV).
C. Program evaluation and review technique (PERT).
D. Scattergraph method.
Answer (B) is correct. Expected value analysis provides a rational means for selecting the
best alternative in decisions involving risk. The expected value of an alternative is found
by multiplying the probability of each outcome by its payoff and summing the products. It
represents the long-term average payoff for repeated trials
In decision making under conditions of uncertainty, expected value refers to the
Likely outcome of A. a proposed action.
B. Present value of alternative actions.
C. Probability of a given outcome from a proposed action.
D. Weighted average of probable outcomes of an action
Answer (D) is correct. The expected value of an action is found by multiplying the
probability of each possible outcome by its payoff and summing the products. It
represents the long-term average payoff for repeated trials. In other words, expected value
is the weighted average of probable outcomes.
In decision theory, those uncontrollable future events that can affect the outcome of a decision
B. States of nature.
Answer (B) is correct. Applying decision theory requires the decision maker to develop
an exhaustive list of possible future events. All possible future events that might occur
must be included, even though the decision maker will likely be very unsure as to which
specific events will occur. These future uncontrollable events are referred to as states of
A widely used approach that managers use to recognize uncertainty about individual items and
to obtain an immediate financial estimate of the consequences of possible prediction errors is
Expected A. value analysis.
B. Learning curve analysis.
C. Sensitivity analysis.
D. Regression analysis.
Answer (C) is correct. Sensitivity analysis determines how a result varies with changes in
a given variable or parameter in a mathematical decision model. For example, in a present
value analysis, a manager might first calculate the net present value or internal rate of
return assuming that a new asset has a 10-year life. The NPV or IRR can then be
recalculated using a 5-year life to determine how sensitive the result is to the change in
The process of evaluating the effect of changes in variables such as sales price or wage rates on
the optimum solution in a linear programming application is called
A. Iterative analysis.
B. Regression analysis.
C. Sensitivity analysis.
D. Matrix analysis
Answer (C) is correct. Sensitivity analysis is a process to determine how sensitive the
final result (solution) is to changes in variables. It is often used in capital budgeting
decisions to incorporate various levels of risk.
Which one of the following techniques would most likely be used to analyze reductions in the
time required to perform a task as experience with that task increases?
A. Regression analysis.
B. Learning curve analysis.
C. Sensitivity analysis.
D. Normal probability analysis.
Answer (B) is correct. Learning curve analysis is used to project productivity gains resulting
from the increased rate at which people perform tasks as they gain experience.
Answer (C) is incorrect. Sensitivity analysis is used to reveal how sensitive expected value
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