The production department of Celltronics International wants to explore the rela

Question

The production department of Celltronics International wants to explore the relationship
between the number of employees who assemble a subassembly and the number produced.
As an experiment, two employees were assigned to assemble the subassemblies. They pro-
duced 1 5 during a one-hour period. Then four employees assembled them. They produced
25 during a one-hour period. The complete set of paired observations follows.


One-Hour
Number of Production
Assemblers (units)
2 1 5
4 25
1 1 0
5 40
3 30


The dependent variable is production; that is, it is assumed that the level of production
depends upon the number of employees.
a. Draw a scatter diagram.
b. Based on the scatter diagram, does there appear to be any relationship between the
number of assemblers and production? Explain.
c. Compute the coefficient of correlation.
d. Evaluate the strength of the relationship by computing the coefficient of determination.

Explanation / Answer

c) The correlation coefficient r is
r = { <xy> - <x><y> } / { (<x2> - <x>2) (<y2> - <y>2) }
where <x> is the average of x

Here it doesn't matter which column are x-values and which column are y-values

d) The coefficient of determination r2 is, well, r2. Zero is uncorrelated, one is perfectly correlated.

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