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. % Worldng 67 45 73 54 61 % Management 50 206645 34 (a) Develop a scatter diagram for these data with the percentage of women working in the company as the independent variable 70 50 50 50 40+ 40 30 30 20 + 20+ 10+ Management Management 10+ 45 50 70 +5 50 65 70 55 60 Working 60 Working O O O 70 60 Management 50 40+ & Management 50 40 30+ 20 30 # 20+ 10+ . 10+ 45 SO 65 70 75 45 50 65 70 55 60 Working 75 55 60 5 Working (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? 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 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. (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.

please assist

Answer 1

50 50 Management 40+ 201 10+ 45 50 55 60 63 70 75 Working

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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,

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70 60 50 40 30 20+ 10+ 45 SO 65 70 75 55 60 5 Working O

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	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	300.00	215.00	480.00	1192.00	672.00
mean	60.00	43.00	SSxx	SSyy	SSxy

Sample size,   n =   5      
here, x̅ = Σx / n=   60.000          
ȳ = Σy/n =   43.000          
SSxx =    Σ(x-x̅)² =    480.0000      
SSxy=   Σ(x-x̅)(y-ȳ) =   672.0      
              
estimated slope , ß1 = SSxy/SSxx =   672/480=   1.4000      
intercept,ß0 = y̅-ß1* x̄ =   43- (1.4 )*60=   -41.0000      
              
Regression line is, Ŷ=   -41.000   + (   1.400   )*x

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Predicted Y at X=   62   is              
Ŷ=   -41.00000   +   1.40000   *62=   45.8

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