Question

Professor John Morton has just been appointed chairperson of the Finance Department at Westland University. In reviewing the department’s cost records, Professor Morton has found the following total cost associated with Finance 101 over the last several terms:
Term Number of
Sections Offered Total
Cost
Fall, last year 7 $ 13,500
Winter, last year 3 $ 8,000
Summer, last year 6 $ 12,000
Fall, this year 2 $ 6,500
Winter, this year 4 $ 10,000
Professor Morton knows that there are some variable costs, such as amounts paid to graduate assistants, associated with the course. He would like to have the variable and fixed costs separated for planning purposes.

Required:

1. Prepare a scattergraph plot. (Place total cost on the vertical axis and number of sections offered on the horizontal axis.)

Instructions:

1. On the graph below, use the point tool (Fall last year) to plot number of sections offered on the horizontal axis and total cost on the vertical axis.

2. Repeat the same process for the plotter tools (winter last year to winter this year).

3. To enter exact coordinates, click on the point and enter the values of x and y.

4. To remove a point from the graph, click on the point and select delete option.

2(a). Using the least-squares regression method, estimate the variable cost per section and the total fixed cost per term for Finance 101. (Round your fixed cost and variable cost to nearest whole dollars.)



2(b). Express these estimates in the linear equation form Y = a + bX. (Round your fixed cost and variable cost to nearest whole dollars.)



3a. Assume that because of the small number of sections offered during the Winter Term this year, Professor Morton will have to offer ten sections of Finance 101 during the Fall Term. Compute the expected total cost for Finance 101. (Do not round your intermediate calculations. Round your final answer to nearest whole dollar.)

Answer 1

Answer and explanation:

1. The scatter plot is attached as an image below

2(a).

Variable cost per section is shown by the slope while

fixed cost is shown by the intercept\

The simple linear regression is as given below

x                    y                    xy                    x²

7                    13,500          94500            49

3                      8000          24000              9

6                    12000           72000           36

2                      6500          13000              4

4                    10000           40000           16

22                  50000          243500        114

Regression Equation: y = a + bx where

x = number of sections offered

y = total cost

a = is the intercept point of regression line and y-axis

b = slope of regression line

N = 5,    ∑x = 22, ∑y = 50000

∑xy = 243500, ∑x² = 114, (∑x)²=484

Slope(b) = ∑xy - ∑x∑y

                  ∑x²- (∑x)²

              =  1366.28 (variable cost per section)

Intercept (a) = ∑y - b∑x

                           N

                    =  3988.37 (fixed cost per section)

2(b).

Writing the expression in the form of an equation

y = a + bx   ⇒    y = 3988 + 1366x

3(a).

Expected Total Cost is calculated by putting the value of x = 10 in the above equation,

Expected Total Cost, y = 3988.37 + 1366.28 × 10 = 17651