Question one
a) The table below gives the interest rates of government bonds sold over a period of 12 months.
Month Interest rate (%) per annum
January 11.5
February 11.3
March 11.4
April 11.6
May 11.8
June 11.7
July 11.8
August 12.5
September 12.0
October 11.7
November 11.6
December 11.6
Required
i) Develop 3-month and 4-month moving averages for this series. (8 marks)
ii) Which moving average provides better forecast? Why? (2 marks)
QUESTION TWO
a) A bakery bakes cakes under the brand name “super cakes.” Irene Juma, the manageress does not know the cost of each cake. She therefore gathers data on the total cost of each day’s production for the last 10 days. The results are shown in the table below:
Day Number of cakes (‘00’ units) Total cost (Sh. ‘000’)
1 22.5 23.0
2 21.0 21.6
3 27.5 23.3
4 21.5 24.0
5 30.0 28.2
6 20.0 22.4
7 24.0 23.1
8 26.5 25.3
9 18.3 20.1
10 17.0 16.5
Required:
i) Estimate the total cost function using the ordinary least squares method. State the fixed cost and unit cost. (11 marks)
ii) If each cake is sold at Sh. 10, determine the break even number of cakes. (3 marks)
b) Two different models are available for the same machine. The production statistics (number of units produced per hour) of these two models are given below. The data was collected on different days.
Model A: 180, 176, 184, 181, 190, 137,
Model B: 195, 194, 190, 192, 187, 185, 187,
Will you conclude that Model A and Model B have the same productivity (6Marks)
QUESTION THREE
The table below shows data on the number of visitors (V) to the Kenyan coastline in a month and the amount of money (M) for each of the 8 months in 2018
Number of visitors V Amount of money spent M (Sh.’M’)
2450 1370
2480 1350
2540 1400
2420 1330
2350 1270
2290 1210
2400 1330
2460 1350
Required
a) Determine the product moment correlation coefficient between number of visitors and amount spent. (4Marks)
b) Give a reason to support fitting a regression model of the form M = a + bv to these data
(2 marks)
c) Find the value of b (4 Marks)
d) Find the equation of the regression line of m and v (4 Marks)
e) Interpret your value of b (2 marks)
f) Use your answer to part (d) to estimate the amount of money spent when the number of visitors to Kenya coastline in a month is 2500. (2 Marks)
g) Comment on the reliability of your estimate in part (f). Give a reason for your answer.
(2 Marks)