Question

Paragraph Question Three a) The table shows the number of people employed in10 small factories and their annual sales in thousands Firm No.of workers 60 25 65 48 35 28 75 50 45 85 Total sales 250 160 108 151 85 96 151 273 241 290 Calculate the Spearman Rank correlation coefficient and comment. A BCDE F G HK b) In Kenya's industrial sector 10 new products have been developed. The cost of developing these products and the corresponding sales and revenue are shown in the following table Product Development Cos(sh. M) 24 23 25 14 21 22 21 18 192 Sales Revenue (Sh. M) 47 49 57 33 43 4 46 35 40 44 (0 Fit the regression of sales revenue in development cost and estimate sales revenue given a development cost of 22.8M (sh.) () Compute the coefficient of determination and comment. c) The amount of cotton grown (Kg.000) in a country during 2013 to 2016 is shown in the following table: Quarter Year 2013 2014 2015 2016 25 22 24 27 28 23 25 29 30 25 27 31 32 27 29 33 By using moving average of suitable order, compute the trendvalues Prtsc Inser F9 禮

Answer 1

a)

SpearMan’s Rank Correlation

Steps

1) Calculate Ranks (in descending order) for both No Of workers and Total Sales and name them as X and Y respectively. Total of d will be zero

2) Then we calculate difference (d) for each Firm

3) Then we sum of D Square

Spearman Rank Correlation is given by:

Hence,

Coefficient = 0.433

The value suggests mild positive correlation

b)

Regression Output

Regression Equation

Sales Revenue = 2.8 + 1.98 * Development Cost

When Development Cost = 22.8

Sales Revenue = 2.8 + 1.98 * 22.8 = 47.96

ii)

Coefficient of Determination = 0.8488 or 84.88%

c)

Steps:

1. First we calculate 4 months moving Average.
2. Then we calculate Centred Average of these 4 months moving Average.