Question

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.

Line Speed	Number of Defective Parts Found
20	24
20	20
30	19
30	16
40	14
40	18
50	13
50	12

(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?

There appears to be a positive relationship between line speed (feet per minute) and the number of defective parts.

There appears to be no noticeable relationship between line speed (feet per minute) and the number of defective parts.   

There appears to be a negative relationship between line speed (feet per minute) and the number of defective parts.

(c)

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

ŷ =

(d)

Predict the number of defective parts found for a line speed of 35 feet per minute.

Answer 1

a.

b. As there is decreasing trend so there is negative relation

There appears to be a negative relationship between line speed (feet per minute) and the number of defective parts.

c.

Sum of X = 280
Sum of Y = 136
Mean X = 35
Mean Y = 17
Sum of squares (SSX) = 1000
Sum of products (SP) = -300

Regression Equation = ŷ = bX + a

b = SP/SSX = -300/1000 = -0.3

a = MY - bMX = 17 - (-0.3*35) = 27.5

ŷ = -0.3X + 27.5

d. For x=35, ŷ = (-0.3*35) + 27.5=17