Apress Better Business Decisions from Data, Statistical Analysis for Professional Success (2014) by Unknown

Author:Unknown
Format: epub
Tags: Management & Leadership, Decision-Making & Problem Solving, Business & Finance, Science & Math, Mathematics, Applied, Statistics
ISBN: 9781484201855
Amazon: 148420185X
Published: 0101-01-01T00:00:00+00:00

CHAPTER

14

Relationships with Numerical Data

Straight Lines, Curved Lines, and Wiggly Lines

It is frequently required to compare two or more sets of data to decide whether they are related in some way. Some quantities are related because we have defined them to be so. Kilometers are related to miles in a precise way and the relationship can be expressed as a formula:

kilometers = miles x 1.609.

Dollars are related to pounds sterling by a precise rate of exchange, which may vary from day to day and place to place, but which is nevertheless precise for a particular transaction. Generally, however, we are dealing with quantities which may show some relationship but rarely a precise relationship.

Scientific investigations under closely controlled laboratory conditions probably come closest to precise relationships, but even here there are small errors involved in making measurements which give uncertainties in the established relationships. At the other end of the scale we may be looking, for example, for a relationship between the way people vote in an election and how their parents vote. Here, it is likely that any relationship is uncertain, and the role of statistical analysis is to quantify the uncertainties.

When a relationship between two variables is sought, a distinction is made between the independent variable and the dependent variable. In Figure 14-1, the relationship between sales of ice cream and daily noon temperature is shown as a line graph. The temperature is the independent variable and sales is the dependent variable, sales depending on the temperature and not the other way round. Line graphs are commonly used, as here, to show relationships, and there is a convention in plotting them with regard to the choice of the quantities to be located on the two axes. The horizontal axis is used for the independent variable and the vertical axis for the dependent variable. Sometimes it is not clear which is which, both variables being dependent on other factors. We may have a choice as to which we treat as the dependent variable and which we treat as the independent variable. If we measure the temperature and humidity at a location at noon each day and plot temperature against humidity, the choice of axes for the two variables will be arbitrary.

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