Question

QUESTION 9 The following data give the percentage of women working (x) in five companies in the retail and trade industry. The percentage of management jobs (y) held by women in each company is also shown. Given that SSy- 1120 62 40 68 49 56 1936 256 3600 1764 781 15605 8340 3844 1600 4624 2728 640 4080 058 15б8 1074 16 60 28 3136 Sum 190 Based on question (8), which of the following statement is correct for the coefficient of determination? 72.43% of the variation in the percentage of working women in the retail and trade industry can be explained by the variation in percentage of management obs held by women by using the estimated regression equation 71.78% ofthe variation in the percentage of working women in the retail and trade industry can be explained by the variation in percentage of management jobs held by women, by using the estimated regression equation. с. 7243% ofthe variation in percentage of management jobs held by women can be explained by he variation in the percentage of working women in the retail and trade industry, by using the estimated regression equation. o D. 71.78% of the variation in percentage of management obs held by women can be explained by the variation in the percentage of working women in the retail and trade industry, by using the estimated regression equation.

Answer 1

$r=\frac{n\sum xy-\sum x\sum y}{\sqrt{\left [ n\sum x^{2} -(\sum x)^{2}\right ]\left [ n\sum y^{2} -(\sum y)^{2} \right ]}}$

$=\frac{(5*11074)-(275*190)}{\sqrt{\left [ (5*15605) -(275)^{2}\right ]\left [ (5*8340) -(190)^{2} \right ]}}$

=0.8511

$r^2=(0.8511)^2=0.7243$