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. If required, enter negative values as negative numbers.
a. Select 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 (to 1 decimal). = + x d. Predict the number of defective parts found for a line speed of 25 feet per minute.

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20 faulty pieces are anticipated to be present when the line speed is 25 feet per minute.

Detailed explanation:

The given information is displayed as follows:

Line Speed; 20, 20, 30, 30, 40, 40, 50, 50

Number of Defective; 23, 21, 19, 16, 15, 17, 14, 11

Parts located

a. The scatter diagram made with Microsoft Excel is attached.

b. The scatter figure appears to show a relationship between increased line speed and the quantity of detected defective parts.

c. The following equation is given for linear regression using the least squares approach;

Y = a + b·X

Where;

b= N∑XY - (∑X)(∑Y)/N∑X^2 - (∑X)^2

a= ∑Y - b∑X / N

We have data from Microsoft Excel;

∑X = 280, ∑Y = 136, ∑X² = 10,800, ∑XY = 4,460, (∑X)² = 78,400, N = 8

By entering the values, we obtain;

b = (8×4,460 - 280×136)/(8×10,800 - 78,400) = -0.3

a = (136 - (-0.3)×280)/8 = 27.5

As a result, we have the following linear regression;

Y = 27.5 - 0.3·X

Consequently, we have when the line speed is 25 feet per minute;

Y = 27.5 - 0.3 × 25 = 20

When the line speed is 25 feet per minute, Y = 20 faulty components should be expected to be identified.

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