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.

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

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

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

Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics 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.

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

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

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.

Four different paints are advertised as having the same drying time. To check the manufacturer’s claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.

$$\begin{matrix} \text{Paint 1} & \text{Paint 2} & \text{Paint 3} & \text{Paint 4}\\ \text{128} & \text{144} & \text{133} & \text{150}\\ \text{137} & \text{133} & \text{143} & \text{142}\\ \text{135} & \text{142} & \text{137} & \text{135}\\ \text{124} & \text{146} & \text{136} & \text{140}\\ \text{141} & \text{130} & \text{131} & \text{153}\\ \end{matrix}$$

At the $\alpha =$ .05 level of significance, test to see whether the mean drying time is the same for each type of paint.

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.

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

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

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.

Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics 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.

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

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

Concur Technologies, Inc., is a large expense-management company located in Redmond, Washington. The Wall Street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city, with an average daily hotel room rate of $198 and an average amount spent on entertainment, including group meals and tickets for shows, sports, and other events, of$172. In comparison, the U.S. averages for these two categories were $89 for the room rate and$99 for entertainment. The following table shows the average daily hotel room rate and the amount spent on entertainment for a random sample of 9 of the 25 most visited U.S. cities (The Wall Street Journal, August 18, 2011).

$$\begin{array}{lcr}\text { City } & \begin{array}{c}\text { Room Rate } \\ (\$)\end{array} & \begin{array}{r}\text { Entertain } \\ \text{ (\$) }\end{array} \\ \text { Boston } & 148 & 161 \\ \text { Denver } & 96 & 105 \\ \text { Nashville } & 91 & 101 \\ \text { New Orleans } & 110 & 142 \\ \text { Phoenix } & 90 & 100 \\ \text { San Diego } & 102 & 120 \\ \text { San Francisco } & 136 & 167 \\ \text { San Jose } & 90 & 140 \\ \text { Tampa } & 82 & 98\end{array}$$

a. Develop a scatter diagram for these data with the room rate as the independent variable.

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

c. Develop the least squares estimated regression equation.

d. Provide an interpretation for the slope of the estimated regression equation.

e. The average room rate in Chicago is $128, considerably higher than the U.S. average. Predict the entertainment expense per day for Chicago.

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.

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.

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