Chapter 2 Bivariate Data Scatterplots

  A scatterplot, which gives a visual display of the relationship between two variables.   In analysing the scatterplot we look for a pattern in the way the points lie.   The patterns tell us that certain relationships exist between the two variables. This is referred to as correlation

  When describing the relationship between two variables displayed on a scatterplot, we need to comment on: (a) the direction — whether it is positive or negative (b) the form — whether it is linear or non- linear (c) the strength — whether it is strong, moderate or weak (d) possible outliers.

Pearson’s Product-moment correlation coefficient   This coefficient is used to measure the strength of linear relationships between variables.   The symbol for Pearson’s product– moment correlation coefficient is r. The value of r.   Ranges from –1 to 1; that is, –1 ≤ r ≤ 1.

  Note that the symbol ≈ means ‘aproximately equal to’. We use it instead of the = sign to emphasise that the value (in this case r) is only an estimate.

The Coefficient of determination   The coefficient of determination is given by r 2.   It is calculated by squaring Pearson’s product–moment correlation coefficient (r).

  The coefficient of determination tells us the proportion of variation in one variable which can be explained by the variation in the other variable. It provides a measure of how well the linear rule linking the two variables (x and y) predicts the value of y when we are given the value of x.   The value is expressed in percentage form.

How to describe the coefficient of determination: The proportion of the variation in ________(y variable) that can be explained by the variation in the _______(x variable) is ___%