Reference no: EM132858069

Budget Analysis I:Production (in 10,000) units: 5 6 7 8 9 10 11

A budget is an expression of management's expectations and goals concerning future revenues and costs. To increase their effectiveness, many budgets are flexible, including allowances for the effect of variation in uncontrolled variables. For example, the costs and revenues of many production plants are greatly affected by the number of units produced by the plant during the budget period, and this may be beyond a plant manager's control. Standard cost-accounting procedures can be used to adjust the direct-cost parts of the budget for the level of production, but it is often more difficult to handle overhead. In many cases, statistical methods are used to predict or forecast overhead from the level of production using historical data.

As a simple example, consider the historical data for a certain plant. Enter the data into EXCEL and analyze it to answer the following items.

Overhead costs (in $1,000): 13 11.9 13 15 15.8 15.2 17.3

(a) Construct a scatterplot of y versus x.

(b) State the model equation.

• OVERHEAD =  ₀ +  ₁PRODUCTION
• PRODUCTION =  ₁ +  ₀OVERHEAD    
• PRODUCTION =  ₁OVERHEAD
• OVERHEAD =  ₁ +  ₀PRODUCTION
• PRODUCTION =  ₀ +  ₁OVERHEAD
• OVERHEAD =  ₁PRODUCTION

In the model equation above, what does OVERHEAD represent?

• The predicted value of the response variable
• The predicted value of the explanatory variable     
• The predicted value of the independent variable
• The predicted value of the predictor variable

In the model equation above, what does  ₀ represent?

• The slope associated with the explanatory variable
• The response variable    
• The explanatory variable
• The model intercept

In the model equation above, what does  ₁ represent?

• The slope associated with the explanatory variable
• The model intercept    
• The response variable
• The explanatory variable

In the model equation above, what is the x-variable?

• The explanatory variable PRODUCTION
• The explanatory variable OVERHEAD    
• The response variable OVERHEAD
• The response variable PRODUCTION

Provide the sample-based estimates for the model parameters. (Round your answers to three decimal places.)

y =  ?  +   ?  x

(c) Graph the regression line on the scatterplot.

(d) Use the model to predict the overhead cost associated with the production of 80,000 units. (Remember, since production is in ten-thousands you need to divide by 10,000 before you plug into the equation. And since cost is in $1000s, you need to multiply the answer you get from plugging into the equation by 1000 to get the answer in dollars. Round your answer to two decimal places.)

$   ?

The actual overhead cost was $15,000 when 80,000 units were produced (See the raw data above). Calculate the residual. (Round your answer to two decimal places.)

$   ?

Interpret the residual you calculated immediately above by mentally inserting the ABSOLUTE VALUE of the residual into the blanks below.

• Our prediction was _______ units higher than the actual overhead cost when 80,000 units were produced. Our prediction was an overestimate.
• When using this model to make predictions, we expect to be off by _______ units, on average.    
• Our prediction was _______ units higher than the actual overhead cost when 80,000 units were produced. Our prediction was an underestimate.
• Our prediction was _______ units lower than the actual overhead cost when 80,000 units were produced. Our prediction was an underestimate.
• Our prediction was _______ units lower than the actual overhead cost when 80,000 units were produced. Our prediction was an overestimate.
• When using this model to make predictions, we expect to be _______ units closer to the true value, on average.