QUESTION 5

All firms struggle with the question of how to limit the number of defective items produced. One firm believes that the number of defectives depends upon three factors - the variation in temperature at the time of production, the rate at which items are being produced, and which shift produces the items (the morning shift believes the afternoon shift are less experienced and the afternoon shift believes the morning shift is less capable).

The quality control officer collected data over thirty (30) shifts on four variables:

1. 1. The number of defective items (per 1000 produced)
2. 2. The variation in the temperature during the shift
3. 3. The rate at which items were produced during the shift (number per hour)
4. 4. Whether or not the shift was the AM or PM shift (AM = 1, PM = 0)

The resulting regression output is provided in the table below:

Summary Output

Regression Statistics

Multiple R

0.948

R Squared

0.899

Adjusted R Squared

0.883

Standard Error

6.644

Observations

30

ANOVA

df

SS

MS

F

P - value

Regression

3

9825.76

3275.25

77.16

0.0001

Residual

26

1103.54

42.44

Total

29

10929.29

Coefficient

Std. Errors

t

P - value (Two Tail)

Intercept

-28.756

60.147

-0.448

0.658

Temperature

26.242

9.051

2.899

0.008

Rate

0.0508

0.126

0.403

0.682

AM/PM

-1.746

0.803

-2.176

0.039

• (a) State clearly the model which is to be tested as well as the estimated equation. Interpret all values.

(5 marks)

(b) Conduct all of the necessary hypothesis tests to determine the usefulness of the model and variables. Write brief report in NON TECHNICAL language summarising the results of these tests and what it means for maintaining quality.

(11 marks)

(c) To what extent does the model not explain the variation in the production of defectives. What statistic did you use to answer this question?

(2 marks)