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 67 45 73 54 61

% Management 49 22 67 45 34

(a)

Develop a scatter diagram for these data with the percentage of women working in the company as the independent variable.

1. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. The first two points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram. Moving to the right, the third point extends downward in a diagonal direction. The last 2 points then extend upward from the third point in a diagonal direction to the right. The points are between 22 to 67 on the vertical axis.
2. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. The first three points are plotted from left to right in an downward, diagonal direction starting in the upper left corner of the diagram. The fourth point extends upward in a diagonal direction to the right. The last point then extends downward from the fourth point in a diagonal direction to the right. The points are between 22 to 67 on the vertical axis.
3. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. The points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 22 to 67 on the vertical axis.
4. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. The points are plotted from left to right in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 22 to 67 on the vertical axis.

(b)

What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

1. 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.
2. 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.
3. 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.

(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.

1. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. A straight line with positive slope is imposed onto the diagram to approximate the relationship between % Working and % Management implied by the points, with 3 points lying below the line. The first two points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram. Moving to the right, the third point extends downward in a diagonal direction. The last 2 points then extend upward from the third point in a diagonal direction to the right. The points are between 22 to 67 on the vertical axis.
2. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. A straight line with negative slope is imposed onto the diagram to approximate the relationship between % Working and % Management implied by the points, with 3 points lying below the line. The first three points are plotted from left to right in an downward, diagonal direction starting in the upper left corner of the diagram. The fourth point extends upward in a diagonal direction to the right. The last point then extends downward from the fourth point in a diagonal direction to the right. The points are between 22 to 67 on the vertical axis.
3. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. A straight line with negative slope is imposed onto the diagram to approximate the relationship between % Working and % Management implied by the points, with 2 points lying below the line. The points are plotted from left to right in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 22 to 67 on the vertical axis.
4. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 40 to 75 and is labeled: % Working. The vertical axis ranges from 0 to 70 and is labeled: % Management. A straight line with positive slope is imposed onto the diagram to approximate the relationship between % Working and % Management implied by the points, with 2 points lying below the line. The points are plotted from left to right in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 22 to 67 on the vertical axis.

(d)

Develop the estimated regression equation by computing the values ofb₀

andb₁.

=

(e)

Predict the percentage of management jobs held by women in a company that has60% women employees.

%