Question

The following data give the percentage of women working in five companies in the retail and trade industry. The percentage of management jobs held by women in each company is also shown. % Working 6745 73 54 61 % Management 51 2364 4632 (a Develop a scatter diagram for these data with the percentage of women working in the company as the independent variable. 20 20 50 . . 50 20 60 50! 60 50 40 60 50 40 Management 40 . 30 30 20 30 20 30 20 10 20 10 10 10 45 50 55 60 65 70 45 50 65 70 75 45 50 65 70 75 45 50 65 70 75 % Working 55 60 % Working 55 60 % Working 55 60 % Working o (b What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? • There appears to be a negative linear relationship between the percentage of women working in the five companies and the percentage of management jobs held by women in each company . There appears to be no noticeable relationship between the percentage of women working in the five companies and the percentage of management jobs held by women in each company • There appears to be a positive linear relationship between the percentage of women working in the five companies and the percentage of management jobs held by women in each company: (c)Try to approximate the relationship between the percentage of women working in the company and the percentage of management jobs held by women in that company. 70 70 60 60 60 50 40 50 40 70 60 50 40 30 50 40 30 30- 30 20 10 20 10 20 10 10 45 50 20 75 55 60 % Working 45 50 65 70 75 45 50 55 50 65 70 75 45 50 65 75 o 55 % Working 55 50 % Working o Working (d Develop the estimated regression equation by computing the values of bo and 61. (e Predict the percentage of management jobs held by women in a company that has 59% women employees. %

Answer 1

Ans a) d)

70 60 50 40 30 20 10 40 45 50 5. 5 60 65 70 75

Ans b)c) There appears to be a positive linear relationship

Explanation: As x tends to increase y tends to increase

Ans c) c)

70 60 50 40 30 20 10 40 45 50 55 60 65 70 75

Ans d)

9 = -31.8+1.253

Ans e) 41.95

Explanation:

Given x = 59

ỳ = -31.8 +1.25 x 59 = 41.95 ans.

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Equation Explanation:

(y-7) (x-x)? (yi-y) (x-7)(y-7) % working (x) % Management (y) 67 51 45 23 (x-X) 7 - 15 7.8 49 60.84 54.6 -20.2 225 408.04 303 73 64 13 20.8 169 432.64 54 46 -6 2.8 36 7.84 270.4 -16.8 - 11.2 61 32 1 - 11.2 1 125.44 60 43.2 Mean() = Mean(y) = sum (xi-x)(yi-y) = sum (xi-x)2 = sum(yi-y)2 = 600 480 1034.8

y = b + b12

b, Σα – Σ). (y - 9 Σ(1 – 1)2

.

600 61 = 1.25 480

bo=y - 51.0

= 43.2 – 1.25 x 60 = -31.8