QUESTION THREE

a) Outline the significance of regression analysis. (4 marks)

b) The following regression results were obtained from an empirical investigation to establish predictors for stock returns in emerging capital markets

Returns = 0.284 + 0.092 market risk + 0.0041 Firm size - 0.022 Firm value

p-value (.104) (.007) (.117) (.000)

Se (2.204) (.0154) (.000853) (.0045)

n = 526, R ² = .316

Where p-values and standard errors appear in parentheses below the estimated coefficients.

Required:

1. Compute the t-statistic for firm value (2 marks)
2. Interpret R-square of the model (2 marks) iii. Interpret the intercept term and coefficients on each independent variable. (4 marks)
3. Use p-values to identify significant predictors of stock returns. (2 marks)
4. Three merchants R, S and M ordered laptops of different brands from Dubai: Hp, Acer and Lenovo. R purchased 10 pieces of Hp, 8 pieces of Lenovo. S purchased 2 pieces of Hp, 6 pieces of Acer and 9 pieces of Lenovo M purchased 4 pieces of Hp, 7 pieces of Acer and 8 pieces of Lenovo. The manufacturer's price for one piece of Hp brand is sh. 40,000, one piece of Acer is sh. 50,000 and one piece of Lenovo is sh.60,000. An important duty of 25% is imposed on each piece at the port of entry. Use matrix operation for find the after-tax amount of money spent by each of the three merchants individually. (6 marks)
5. (e) A firm uses two machines in the manufacture of two products A and B. Each unit of product A requires 1 hour and 2 hours on machine 1 and II respectively. Each unit of product B requires 2 hours and 1 hour on machine 1 and II respectively. It is required that product A units should not exceed 320. The contribution margin on product A and B is Sh.6 and Sh.4 per unit respectively. The machine hours available on the two machines 1 and II are 720 and 780 respectively. Required: -
6. i. Formulate the above problem as a linear programming problem. [4 Marks]
7. ii. Develop the first simplex tableau for the problem [4 Marks

QUESTION FOUR

a) Discuss important assumptions of the Linear programming model. (3 marks)

b) Explain the following concepts as used in hypothesis testing

i. Significance level (2 marks)

ii. Parametric test (2 marks)

1. A statistic (2 marks)

c) A sales man has the following record of sales during three months for three items A, B and C which have different rates of commission

Months	Sales in units A	Sales in units B	Sales in units C	Total Sales (Ksh.)
January	90	100	20	800
February	130	50	30	900
March	60	100	40	850

Let X1, X2 and X3 be the selling price unit in sh. on item A, B and C respectively.

d) Formulate a system of simultaneous equations for the above information. (3 marks)

e) Use matrix algebra to determine the selling price per unit of each item. (3 marks)