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Interpreting Data
5.2 What types of relationship might exist between two quantitative variables?
5.2.1 Deterministic relationship
In some circumstances, if we know the value of one variable we can calculate the exact value of another. The relationship between the two variables is deterministic and is governed by a mathematical function. In such a deterministic relationship, there is perfect association between the variables. This is not usually the case for relationships measured between variables in contexts which involve sampled data. An example of such a deterministic relationship is when two variables measure the same thing but on different scales. Temperature measurements on the Fahrenheit scale (F) and on the Celsius scale (C) are such a relationship which is represented by the equation F = 32 + 1.8 C
5.2.2 Statistical relationship
This is measured according to how well an explanatory (predictor) variable can explain the variability in a response variable. The statistical tools used in investigating such a relationship include:
- a scatterplot graph of the bivariate data - just as we drew graphs of univariate data - this is a most important starting point;
- the regression line (least squares line) which indicates the trend of the data - much like the measures of central tendency for univariate data (mean and median) indicate the centre of a univariate data set;
- correlation (co-relation) - which measures the strength of the association by the closeness of the data points to the regression line - just as the standard deviation described how far away the data points of a univariate data set are from the mean.
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