Question

Question 3 (a)

The business objective of the director of planning of Game Ghana is to forecast monthly sales for all new stores, based on the number of profiled customers who live no more than 30 minutes from a Game store. To examine the relationship between the number of profiled customers who live within a fixed radius from a Game store and its monthly sales, data were collected from a sample of 10 stores:

Store

No. of Customers (‘000) Monthly Sales (‘000)

1 2 3 4 5 6 7 8 9 10 5 7 2 8 4 3 2 4 5 3 8 12 6 14 8 7 9 10 12 8

(i) Use the least-squares method to compute the regression coefficients ? and ?.

(ii) Write down the estimated equation and predict the monthly sales if there are 9000

customers.

(iii) Determine the coefficient of determination, ? , and explain its meaning in this problem.

(iv)Determine the value of the extent of relationship between annual sales and number of customers, and interpret your result.

Question 3 (b)

The Coca-Cola Company is an American multinational corporation, and manufacturer, retailer, and marketer of non-alcoholic beverage concentrates and syrups. The company is best known for its flagship product Coca-Cola, invented in 1886 by pharmacist John Stith Pemberton in Atlanta, Georgia. In Ghana, the company was formed from a divestiture of Bottling Division of G.N.T.C in March 1995 and started operations on March 7, 1995 at the GNTC plant at Adjabeng. The new premises sited off the Spintex Road, was commissioned in 1996. Since the divestiture, the Company has invested over US$90 million in vehicles, glass bottles, plastic bottles, plastic crates, production and marketing equipment. In 2019, the company contracted an economist who estimated the demand function for the company’s product (Coca-Cola) using data from 28 supermarket as follows:

?= +0.5?−24=0

where P is the price per bottle and ?= is the quantity demanded. In addition, the economist also

estimated the supply function for product as follows.

4?> − 3? + 4 = 0

where P is the price per bottle and ?> is the quantity supplied. As the consultant of this

company, you are to use this information to:

(i) Determine the equilibrium level of price and quantity

(ii) Represent your answer graphically by sketching the demand and supply curves.

(iii) Determine the welfare of economic agents using integration

(iv)Suppose the government imposes a tax of ¢4 one very bottle sold,determine the new equilibrium price and quantity

(v)How will the consumers and producers share the tax per unit?

Answer 1

Answer : 3 (a)

(i) Calculation of regression coefficients ? and ? Using least-squares method :

Store	X	Y			XY
1	5	8	25	64	40
2	7	12	49	144	84
3	2	6	4	36	12
4	8	14	64	196	112
5	4	8	16	64	32
6	3	7	9	49	21
7	2	9	4	81	18
8	4	10	16	100	40
9	5	12	25	144	60
10	3	8	9	64	24
Total	43	94	221	942	443

From above,

ΣX = 43

ΣY = 94

ΣXY = 443

a = 4.778

b = 1.075

So, Regression coefficient a = 4.778

Regression coefficient b = 1.075

(ii)

Estimated Equation Is  Y = 4.778 + 1.075X

If there are 9000 Customers, then monthly sales will be

X = 9

Y = 4.778 + 1.075 x 9

Y = 14.453

So, If there are 9000 Customers, then monthly sales will be 14,453

(iii) Calculation of coefficient of determination

Coefficient of Correlation =

= 0.845

Coefficient of determination    = 0.7140 = 71.40%

Coefficient of determination determines the percentage of variation accounted by factor under consideration.

So, In above case this means that 71.40% change in Monthly Sales has been accounted by Number of Customers.

(iv) The Value of the extent of relationship between annual sales and number of customers is represented by the Coefficient of correlation and it is 0.845

Interpretion

Because Coefficient of correlation is Positive and it is near to 1, We can conclude that there is positive relationship between annual sales and number of customers and this relationship is strong.