Suppose
I can measure the number of times incorrect information was provided to
customers from our service department (labeled E for number of
errors). We have noticed with
concern that E has been increasing steadily so we began initiating
training for our service team. The
number of hours of training completed is designated by T. Based on data analysis we have estimated
the following relationship between E and T to be:
E = 1800 – 20T + 2T2
(3 points) Graph this function. What is the intercept and slope of this
equation, and provide interpretations of both these within the context of
this problem.
(2 points) Does this
functional form seem
reasonable? Explain fully – really
think about the variables and how they are likely related.
(2 points) What level of training (T) would
minimize the number of errors produced (E)? What is the value of the minimum number
of errors? Show all your work and
explain the economics behind
the steps!
(1 point). Suppose
we are still concerned with the number of errors and are thinking about
switching to a different set of training tutorials that we thing would be
more effective. If the new
tutorials are indeed more effective we would see a change to the function
identified above. Specifically, the
-20T could change, and/or the +2T2 could change. Intuitively, what is the difference
between these two terms changing?
Hint: functions are all
about relationships – so when the function changes it is saying that the
relationship is changing. There are different ways the relationship can
change and this is the focus of the question.
(2 points) What is a relationship between
two variables in your professional or personal life that you would like to
be able to estimate? What are the
two variables, how are they measured, and do you believe the relationship
is linear or non-linear (explain why)?
Lastly, what is your motivation for gathering this specific
information?
