ighLow Method Method of Least Squares Correlation Big Mikes

igh-Low Method, Method of Least Squares, Correlation

Big Mike’s, a large hardware store, has gathered data on its overhead activities and associated costs for the past 10 months. Nizam Sanjay, a member of the controller’s department, believes that overhead activities and costs should be classified into groups that have the same driver. He has decided that unloading incoming goods, counting goods, and inspecting goods can be grouped together as a more general receiving activity, since these three activities are all driven by the number of receiving orders. The 10 months of data shown below have been gathered for the receiving activity.

Required:

1. Choose the correct scatter graph that represents the data provided above.

The correct answer is

2. Select two points (1 and 8) that make the best fit, and compute a cost formula for receiving costs. Round intermediate calculations to the nearest cent. Round the intercept to the nearest dollar and round the slope to the nearest cent.

3. Using the high-low method, prepare a cost formula for the receiving activity. Round the intercept to the nearest dollar and round the slope to the nearest cent.

4. Using the method of least squares, prepare a cost formula for the receiving activity. Round the intercept to the nearest dollar and round the slope to the nearest cent.

What is the coefficient of determination? Round your answer to two decimal places.
Adjusted R² =

Month	Receiving Orders	Receiving Cost
1		1,000		$12,170
2		1,340		12,940
3		1,150		13,750
4		900		9,930
5		1,350		15,070
6		1,400		14,145
7		1,600		16,640
8		1,490		14,800
9		1,800		17,940
10		1,700		15,000

Solution

Answer

1.

The answer is C as Graph C represents the correct data.

Graph a, b and d cannot be right as in Graph b there is no no. of received between 1500 and 2000 which is not true and in Graph d there is less than 500 received order which is not true either. Graph a cannot be true as we know that when we received 1600 orders the cost is more than 16k but on graph it is wrongly represented Graph a is also not right.

So correct Option is C

2.

.

Orders received

Cost

1

1000

12,170

8

1490

14,800

Difference

490

2,630

Variable cost = Difference in Cost / Difference in Orders

= 2,630 / 490

Variable cost = $5.367 per order received

Fixed Cost = Total Cost – Variable cost

Let’s take 1 month, Total Cost = $12,170, Order Received = 1000

Fixed Cost = $12,170– (1000 orders * $5.367 per patient)

Fixed Cost = $6,803

Y = $6,803 + $5.367X

Y= Total Cost

X= No. of Orders received

3.

High-Low Method

As we can see that in 9^th month the orders received is highest and In 4^th Month the orders received is Least.

Month

Orders Received

Cost

9^th

1800

17,940

4^th

900

9,930

Difference

900

8,010

Variable cost = Difference in Cost / Difference in order received

= 8010 / 900

Variable cost = $8.9 per patient admitted

Fixed Cost = Total Cost – Variable cost

Lets take 9^th month, Total Cost = $17,940, Order received = 1800

Fixed Cost = $17,940 – (1800 Patients * $8.9 per patient)

Fixed Cost = $1,920

Y = $1,920 + $8.9X

Y= Total Cost

X= No. of Orders received

4.

x

y

X²

xy

        1,000

     12,170

     1,000,000

     12,170,000

        1,340

     12,940

     1,795,600

     17,339,600

        1,150

     13,750

     1,322,500

     15,812,500

           900

        9,930

         810,000

       8,937,000

        1,350

     15,070

     1,822,500

     20,344,500

        1,400

     14,145

     1,960,000

     19,803,000

        1,600

     16,640

     2,560,000

     26,624,000

        1,490

     14,800

     2,220,100

     22,052,000

        1,800

     17,940

     3,240,000

     32,292,000

        1,700

     15,000

     2,890,000

     25,500,000

     13,730

   142,385

   19,620,700

   200,874,600

N= 10

?x = 13,730

?y = 142,385

?x2 = 19,620,700

?xy = 200,874,600

Unit Variable cost (b) = (n.?xy – ?x.?y) / [n?x² – (?x)²]

= (10 * 200,874,600 - 13,730 * 142,385) / [10 * 19,620,700 – (13,730)²]

Variable cost (b) = $6.99236 per order

Fixed Cost (a) = (?y – b?x) / n

= (142,385 - $6.99236 * 13,730) / 10

Fixed Cost = $23,839.016

Y = $23,893 + $6.99X

Y= Total Cost

X= No. of Orders received

5.

Coefficient =

= 53799950 / 59381997.36

Coefficient = 0.91

	Orders received	Cost
1	1000	12,170
8	1490	14,800
Difference	490	2,630