Chapter 5, Problem 62P

Interpretation of Regression Results: Multiple Choice

The Business School at Eastern College is collecting data as a first step in the preparation of next year’s budget. One cost that is being looked at closely is administrative staff as a function of student credit hours. Data on administrative costs and credit hours for the most recent 13 months follow:

The controller’s office has analyzed the data and given you the results from the regression analysis:

Required

1. a.      In the standard regression equation y = a + bx, the letter b is best described as the:
   1. (1) Independent variable.
   2. (2) Dependent variable.
   3. (3) Constant coefficient.
   4. (4) Correlation coefficient.
   5. (5) Variable cost coefficient.
2. b.      In the standard regression equation y = a + bx, the letter y is best described as the:
   1. (1) Independent variable.
   2. (2) Correlation coefficient.
   3. (3) Constant coefficient.
   4. (4) Variable cost coefficient.
   5. (5) Dependent variable.
3. c.       In the standard regression equation y = a + bx, the letter x is best described as the:
   1. (1) Independent variable.
   2. (2) Dependent variable.
   3. (3) Constant coefficient.
   4. (4) Variable cost coefficient.
   5. (5) Correlation coefficient.
4. d.      If the controller uses the high-low method to estimate costs, the cost equation for administrative costs is (numbers are rounded to the nearest dollar):
   1. (1) Cost = $291,637 + (229 × Credit hours).
   2. (2) Cost = $233,571 + (101 × Credit hours).
   3. (3) Cost = $229.50 × Credit hours.
   4. (4) Cost = $404,874.
   5. (5) Some other equation.
5. e.       Based on the results of the controller’s regression analysis, the estimate of administrative costs in a month with 2,100 credit hours would be:
   1. (1) $834,993.
   2. (2) $844,200.
   3. (3) $404,917.
   4. (4) $839,575.
   5. (5) Some other amount.
6. f.        The correlation coefficient (rounded) for the regression equation for administrative costs is:
   1. (1) 0.871.
   2. (2) 0.933.
   3. (3) 0.859.
   4. (4) $\sqrt{0.933}$.
   5. (5) Some other amount.
7. g.      The percent of the total variance (rounded) that can be explained by the regression is:
   1. (1) 85.9.
   2. (2) 87.1.
   3. (3) 93.3.
   4. (4) 96.6.
   5. (5) Some other amount.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 62P

Option (5) The letter b is described as variable cost coefficient.

Explanation of Solution

Variable cost coefficient:

Variable cost coefficient is the per unit cost of x. Total cost is calculated by adding the fixed cost and variable cost. The variable cost coefficient is multiplied by its respective activity to calculate the total variable cost at a given point.

Justification for the correct and incorrect answer:

(1)

Independent variable: This is an incorrect figure as the x is the independent variable.

(2)

Dependent variable: This is an incorrect figure because y is the dependent variable.

(3)

Constant coefficient: This is an incorrect option because the given equation does not contain constant coefficient.

(4)

Correlation coefficient: This is incorrect because the given equation does not contain a constant coefficient.

(5)

Variable cost coefficient: This is the correct option because b is a variable cost coefficient.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 62P

Option (5) The letter y is described as Dependent variable.

Explanation of Solution

Dependent variable:

The dependent variable is the figure that is based on the variance of fixed and variable cost. It is calculated by adding the fixed and variable cost of the respective activity.

Justification for the correct and incorrect answer:

(1)

Independent variable: This is an incorrect figure as the x is the independent variable.

(2)

Correlation coefficient: This is incorrect because the given equation does not contain the correlation coefficient.

(3)

Constant coefficient: This is an incorrect option because the given equation does not contain constant coefficient.

(4)

Variable cost coefficient: This is an incorrect option because b is a variable cost coefficient.

(5)

Dependent variable: This is the correct option because y is the dependent variable.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 62P

Option (1) The letter x is described as Independent variable.

Explanation of Solution

Independent variable:

The independent variable is not dependent on any other variable. It is used to calculate the total variable cost of the activity.

Justification for the correct and incorrect answer:

(1)

Independent variable: This is the correct figure as the x is the independent variable.

(2)

Dependent variable: This is an incorrect option because y is the dependent variable.

(3)

Constant coefficient: This is an incorrect option because the given equation does not contain constant coefficient.

(4)

Variable cost coefficient: This is an incorrect option because b is a variable cost coefficient.

(5)

Correlation coefficient: This is incorrect because the given equation does not contain the correlation coefficient.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 62P

Option (1) The administrative cost equation is:

$\text{Administrative cost = \$291,637 + (\$229 }\times \text{ number of credit hours)}$.

Explanation of Solution

Administrative cost:

Administrative cost is the cost of the expenses which are incurred for activities other than production and sales. These expenses are related to the executives and general services of the entity.

Calculate the administrative cost:

Show the cost equation of fixed and variable cost with the overhead cost:

$\begin{array}{c}\text{Administrative cost = Fixed cost + Variable cost}\\ \text{= \$291,637 (1) + (\$229 (2) }\times \text{ number of credit hours)}\end{array}$

Thus, the cost equation is:

$\text{Administrative cost = \$291,637 + (\$229 }\times \text{ number of credit hours)}$.

Working note 1:

Calculate the fixed cost:

$\begin{array}{c}\text{Fixed cost = Total cost - Variable cost}\\ \text{= }\$960,036\text{ - \$668,399 (3)}\\ =\text{ \$291,637}\end{array}$

Calculate the highest and lowest activity:

Particular	Credit hours	Administrative costs
Highest activity	2,923	$960,036
Lowest activity	242	$346,975

Table: (1)

Working note 2:

Calculate the variable cost (unit) with the help of high-low cost method:

$\begin{array}{c}\text{Variable cost = }\frac{\mathrm{Co}\text{st of highest activity }-\text{ Cost of lowest activity}}{\text{Highest activity units }-\text{ Lowest activity units}}\\ =\frac{\begin{array}{c}\$960,036–\$346,975\end{array}}{2,923–242}\\ =\text{ \$228}\text{.6688 per unit}\end{array}$

Working note 3:

Calculate the variable cost ($) with the help of high-low cost method:

$\begin{array}{c}\text{Variable cost (\$) = Credit hours }\times \text{ Rate per unit}\\ \text{= 2,923 }\times \text{ \$228}\text{.6688(2)}\\ \text{= \$668,399}\end{array}$

Justification for the correct and incorrect answer:

(1)

$\text{Cost = \$291,637 + (229 }\times \text{ Credit hours)}\text{.}$ : This is correct figure it is the same as per the given calculation.

(2)

$\text{Cost = \$233,571 + (101 }\times \text{ Credit hours)}$ : This is an incorrect option because the fixed cost is $291,637.

(3)

$\text{Cost = \$229}\text{.50 }\times \text{ Credit hours}$ : This is an incorrect option because the variable cost is missing.

(4)

$\text{Cost = \$404,874}\text{.}$ : This is an incorrect option because there is no variable cost.

(5)

Some other equation: This is incorrect because the answer is one from one of the above options.

To determine

Identify the appropriate answer for the given statement from the given choices.

Answer to Problem 62P

Option (4) The administrative cost is $839,575

Explanation of Solution

Administrative cost:

Administrative cost is the cost of the expenses which are incurred for activities other than production and sales. These expenses are related to the executives and general services of the entity.

Calculate the administrative cost:

$\begin{array}{c}\text{Administrative cost = \$291,637 + (\$229 }\times \text{ number of credit hours)}\\ \text{= \$291,637 + (\$229 }\times \text{ 2,100)}\\ \text{= \$839,575}\end{array}$

Thus, the administrative cost is $839,575.

Justification for the correct and incorrect answer:

(1)

$834,993: This is an incorrect figure because the administrative cost is $839,575.

(2)

$844,200: This is an incorrect option because it is not matching with the calculated cost of administration.

(3)

$404,917: This is an incorrect option as the figure is not matching with the calculated figure of $839,575.

(4)

$839,575: This is the correct option because the administrative cost is $839,575.

(5)

Some other equation: This is incorrect because the answer is one from one of the above options.

To determine

Find out the correct option out of all the given options.

Answer to Problem 62P

Option (2) The correlation coefficient is the “Multiple R,” 0.933.

Explanation of Solution

Correlation coefficient:

Correlation coefficient calculates a linear relationship between two variables and forms an equation to calculate a variable at various level of the output of another variable.

Justification for the correct and incorrect answer:

(1)

0.871.: This is an incorrect figure because it is the value of R.

(2)

0.933: This is an incorrect option because it is the value of multiple R.

(3)

0.859: This is an incorrect option because it is the value of adjusted R.

(4)

$\sqrt{0.933}$ : This is an incorrect option because the correct value is 0.944

(5)

Some other equation: This is incorrect because the answer is one from one of the above options.

To determine

Find out the correct option out of all the given options.

Answer to Problem 62P

Option (2) The percent of the total variance (rounded) that can be explained by the regression is 87.1%.

Explanation of Solution

The coefficient of determination (R²):

The coefficient of determination shows the change in the variation in Y with the change in the variable of X. It is also known as R².

Justification for the correct and incorrect answer:

(1)

85.9.: This is an incorrect figure because it is the value of the adjusted R square.

(2)

87.1: This is the correct option because it is the value of R square.

(3)

93.3: This is an incorrect option because it is the value of multiple R.

(4)

96.6: This is an incorrect option because of the correct value 87.1.

(5)

Some other equation: This is incorrect because the answer is one from one of the above options.