Production Line Speed and Quality Control. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

Number of Defective

$$\begin{array}{cr}\begin{array}{lr}\text { Line } \\ \text { Speed }\end{array} & \begin{array}{r}\text { Defective } \\ \text { Parts Four }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$$

Develop a scatter diagram with the line speed as the independent variable.

Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

$$\begin{array}{cc}\begin{array}{c}\text { Line } \\ \text { Speed }\end{array} & \begin{array}{c}\text { Number of } \\ \text { Defective } \\ \text { Parts Found }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$$

a. Develop a scatter diagram with the line speed as the independent variable.

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

c. Use the least squares method to develop the estimated regression equation.

d. Predict the number of defective parts found for a line speed of 25 feet per minute.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Given are five observations for two variables, x and y.

$$\begin{matrix} x_i & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \hline y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Develop the estimated regression equation for these data.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Use the estimated regression equation to predict the value of y when x = 6.

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.

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

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

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.

d. Develop the estimated regression equation by computing the values of $b_0$ and $b_1$.

e. Predict the percentage of management jobs held by women in a company that has 60% women employees.

Use the least squares method to develop the estimated regression equation.

Use the least squares method to develop the estimated regression equation.

Given are five observations for two variables, x and y.

$$\begin{matrix} x_i & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \hline y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$$

Try to approximate the relationship between x and y by drawing a straight line through the data.

Given are five observations for two variables, x and y.

$$\begin{matrix} x_i & \text{3} & \text{12} & \text{6} & \text{20} & \text{14}\\ \hline y_i & \text{55} & \text{40} & \text{55} & \text{10} & \text{15}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Given are five observations for two variables, x and y.

$$\begin{matrix} x_i & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \hline y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$$

Use the estimated regression equation to predict the value of y when x = 4.

Given are five observations collected in a regression study on two variables.

a. Develop a scatter diagram for these data.

b. Develop the estimated regression equation for these data.

c. Use the estimated regression equation to predict the value of y when x=6.

Given are data for two variables, x and y.

$$\begin{matrix} x_i & \text{6} & \text{11} & \text{15} & \text{18} & \text{20}\\ y_i & \text{6} & \text{8} & \text{12} & \text{20} & \text{30}\\ \end{matrix}$$

Develop an estimated regression equation for these data.