Question

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.
Line Speed Number of Defective Parts Found
20 23
20 21
30 19
30 16
40 15
40 17
50 14
50 11

Required:
a. Use the least squares method to develop the estimated regression equation (to 1 decimal).
b. Predict the number of defective parts found for a line speed of 25 feet per minute.

Answer 1

Answer:

a. y = 27.5 - 0.3X

b. 20

Step-by-step explanation:

y =  a + bX

usin the table in the attachment i added, we so for the regression equaion

n = 8

∑xy = 4460

∑x = 280

∑y = 136

∑x²= 10800

$b=\frac{8(4460)-(280)(136)}{8(10800)-280^{2} } \\b=\frac{35680-38080}{86400-78400} \\b=\frac{-2400}{8000} \\b = -0.3$

from here we solve for a

$a= \frac{136-(-0.3)(280)}{8} \\a =\frac{136+84}{8} \\a=\frac{220}{8} \\a = 27.5$

a. the estimated regression equation

y = 27.5 - 0.3X

b. at x = 25

y = 27.5 - 0.3(25)

y = 20 is the number of defective parts.