Business Statistics: Chapter 14 1) Given are five observations for two variables, x and y . x i 1 2 3 4 5 y i 3 7 5 11 14 a. Which of the following scatter diagrams accurately represents the data? 1. 2.
3. SelectScatter diagram #1Scatter diagram #2Scatter diagram #3Item 1 b. What does the scatter diagram indicate about the relationship between the two variables? Select There appears to be a linear relationship between x and y c. Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal). Y= .2 + 2.6x
d. Use the estimated regression equation to predict the value of y when x = 4 (to 1 decimal). = 10.6 2) Given are five observations collected in a regression study on two variables. Excel file: data14-03.xls a. Which of the following scatter diagrams accurately represents the data? Scatter diagram #1 Scatter diagram #2
Scatter diagram #3 - Select your answer Scatter diagram #1 b. Compute b 0 and b 1 (to 1 decimal). b 1 .9 b 0 7.6 Complete the estimated regression equation (to 1 decimal). = + x y= 7.6 + .9x
c. Use the estimated regression equation to predict the value of y when x = 6 (to 1 decimal). = Y=13
2) 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: data14-05.xls If required, enter negative values as negative numbers.
a. Select a scatter diagram with the line speed as the independent variable. Scatter diagram 1
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? negative it is negative because the x variable is negative, therefore negative slope c. Use the least squares method to develop the estimated regression equation (to 1 decimal). Y= 27.5 + -0.3x I got this on my ti-84 by adding all information in L1 L2 then calculate, 8:linreg(a+bx) d. Predict the number of defective parts found for a line speed of 25 feet per minute. 27.5 -0.3(25) =20 =20
3) Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011 Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. The following data show the number of cars in service (1000s) and the annual revenue ($millions) for six smaller car rental companies ( Auto Rental News website, August 7, 2012).