Quick questions on Scatterplots and bivariate data for HSC Maths Standard 2

A scatterplot is a graph of one variable against another with each data point plotted as a single dot. By convention:

State all three when describing a scatterplot. Markers expect explicit use of these words.

An outlier is a point that lies far from the bulk of the data. Outliers can dramatically affect the calculated correlation coefficient and the regression line.

A strong positive correlation between $x$ and $y$ does not prove that $x$ causes $y$. A third variable may explain both. Standard 2 expects you to mention this whenever a worded question invites a causal claim.

:::worked Worked example ### Constructing from a table

Imagine ABS data on the relationship between household weekly spending on housing ($x$) and on entertainment ($y$). The scatterplot might show:

A scatterplot of car fuel efficiency ($x$, L per $100$ km) and CO$_2$ emissions ($y$, g per km) shows a clear positive linear relationship except for one electric vehicle plotted at $(0, 0)$. The EV is an outlier because the relationship breaks down for non-internal-combustion vehicles. Remove the EV from the dataset if you only want to model petrol/diesel vehicles, or note explicitly that the model only applies to that subgroup. :::

A scatterplot is a set of dots, not a line graph. Do not join them.

A strong correlation does not prove $x$ causes $y$. Use cautious language ("associated with", "tends to") unless the question gives you a causal mechanism.

Always identify any obvious outliers and comment on whether they should be kept or removed.

Independent variable on $x$, dependent on $y$. Mixing this up changes the interpretation. :::