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\f2 . +16 +12 +8 +4 -05 05 1 15 2 25 3 35 4 45 5 55 X t-4 3. -16 +12 +8 -4 05.. J.05 4 15 2 25 3 35 4 45 5 55 X 1-4 Scatter diagram #3b. What does the scatter diagram indicate about the relationship between the two variables? There appears to be a M linear relationship between as and y. c. Try to approximate the relationship between :1: and y by drawing a straight line through the data. Which of the following scatter diagrams with a trend line accurately represents the data? \fd. Develop the estimated regression equation by computing the values of be and b] using Equation 14.6 and Equation 14.7 (to 1 decimal). 669.0 0 + 0.157 0:1: 1? e. Use the estimated regression equation to predict the value of y when :1: = 3 (to 1 decimal). 1450 0 a? Given are five observations for two variables, :0 and y. 3. Choose the correct scatter diagram for these data: A. 60 50 4O 30 20 10 414 7 58 48 58 60 50 4O 3O 20 19 12 16 19 60 50 40 30 20 . 10 60 50 4O 3O 2O 10 b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a w linear relationship between :1: and y. c. Try to approximate the relationship between :L' and y by drawing a straight line through the data. l Many different straight lines can be drawn v] w to provide a linear approximation of the relationship between :L' and y. d. Develop the estimated regression equation by computing the values of be and in using equations: (Enter negative values as negative figure) 2(31 5X95 3) b1 = ' 2 (mi 32 b0 = y 1715 g) = 78.82 0 + 3.15 0 :c (to 2 decimals) e. Use the estimated regression equation to predict the value of y when a: = 5. 63.07 0 (to 2 decimals) 1? 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 55 62 % Management 22 66 48 34 a. From the following select the appropriate scatter diagram for these data with the percentage of women working in the company as the independent variable. Scatter diagram a %Management -60 -50 1p 20 30 4o 50 op %Wadln'ng Scatter diagram b %Management -60 -50 -40 -30 -20 -10 10 20 30 40 50 60 % Working Scatter diagram c %Management -60 -50 -40 -30 -20 -10 10 20 30 40 50 60 % Working Scatter diagram cb. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? Positive linear relationship V w c. Try to approximate the relationship between the percentage of the women working in the company and the percetage of the management jobs held by women in that company. Many different straight lines can be drawn to provide a M approximation of the relationship between in and y. d. Develop the estimated regression equation by computing the values b0 and in. Enter negative values as negative numbers. Do not round intermediate calculations. Round your answers to one decimal place. 3): 35.2 0+ 1.3 \\'92 e. Predict the percentage of management jobs held by women in a company that has 60% women employees. Do not round intermediate calculations. Round your answers to nearest whole value. 42.8 0 % 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. Excel file: data 14-05.xlsx Number of Line Defective Speed Parts Found 20 23 20 21 30 19 30 16 40 15 40 17 50 14 50 11 If required, enter negative values as negative numbers. a. Select a scatter diagram with the line speed as the independent variable. A. Number of Defective Parts 25 20 15 o 10 -1 O -5 5 10 15 20 25 30 35 4O 45 50 55 '5 Line Speed {feet per minute: Number of Defective Parts 25 20 15 10 -1 0 -5 5 10 15 20 25 30 35 4O 45 50 55 Line Speed {feet per minutei 1.v_L Number 25 20 15 10 Number 25 20 15 10 of Defective Parts 10 15 Line 20 Speed of Defective Parts 10 15 Line 20 Speed 25 (feet 25 (feet 30 per 30 per 35 minute: 35 minute l 40 40 45 45 50 50 55 55 b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? Negative relationship V w c. Use the least squares method to develop the estimated regression equation (to 1 decimal). = 83.1 0 + 2.8 0 :L' . Predict the number of defective parts found for a line speed of 25 feet per minute. 690 RE) A B C D E F G H K 1 Number of Defective Line Speed Parts Found 2 20 23 3 20 21 4 30 19 30 16 6 40 15 J 40 17 8 50 14 9 50 11The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yds/Att) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season (NFL website). Team Yds / Att WinPct Arizona Cardinals 7.2 51 Atlanta Falcons 6.4 36 Carolina Panthers 7.9 60 Chicago Bears 7.4 46 Dallas Cowboys 7.0 41 New England Patriots 5.4 14 Philadelphia Eagles 8.3 66 Seattle Seahawks 7.4 51 St. Louis Rams 6.9 37 Tampa Bay Buccaneers 8.4 70a. Choose the correct a scatter diagram with the number of passing yards per attempt on the horizontal axis and the percentage of games won on the vertical axis. A. - . B. - . Wm Pct Wm Pct 80 80 70 I 70 I o o 60 O 60 0 50 I I 50 I I I I 40 ' 4o ' I ' o . 30 30 20 20 C C 10 10 C. `WinPct D. WinPct -80+ -80+ 70+ 70+ 60+ 60+ 50+ 50+ 40+ 40+ 30+ 30+ 20+ 20+ 10+ 10+ 5 6 7 8 9 15 6 7 8 9 Yds/Att Yds/Att Ab. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a 9 linear relationship between m = average number of passing yards per attempt and y = the percentage of games won by the team. c. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt. Enter negative value as negative number. WinPct = 0 +( 0)(Yds/Att) (to 4 decimals) d. Provide an interpretation for the slope of the estimated regression equation (to 1 decimal). The slope of the estimated regression line is approximately 0. So, for every w of one yard in the average number of passes per attempt, the percentage of games won by the team increases by 0%. e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was was 7.3. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note.- For the 2011 season the Kansas City Chiefs' record was 7 wins and 9 losses.) 0 % (to 2 decimals) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs. Considering the small data size, the prediction made using the estimated regression equation w