2.4 TWO VARIABLE RELATIONSHIPS

what is an Associated Variables?

Two variables are associated if values of one variable tend to be related to values of the other variable.

what are Causally Associated Variables?

Two variables are causally associated if changing the value of the explanatory variable influences the value of the response variable.

**Association does not necessarily imply causation!!!!!

what are side-by-side graphs?

Side-by-side graphs are used to visualize the relationship between a quantitative variable and a categorical variable. The side-by-side graph includes a graph for the quantiative variable (such as a boxplot, histogram, or dotplot) for each group in the categorical variable, all using a common numeric axis.

what is a scatterplot?

A scatterplot is a graph of the relationship between two quantitative variables.

• A scatterplot includes a pair of axes with appropriate numerical scales, one for each variable.

• The paired data for each case are plotted as a point on the scatterplot.

where do we put the explanatory variable?

we put the explanatory variable on the horizontal axis and the response variable on the vertical axis.

What do we look for when looking at a scatterplot?

Do the points form a clear trend with a particular direction, are they more scattered about, or is there no obvious pattern?

what does a positive association mean?

that values of one variable tend to be higher when values of the other variable are higher.

what does a negative association mean?

means that values of one variable tend to be lower when values of the other variable are higher.

what is true about two variables?

Two variables are not associated if knowing the value of one variable does not give you any information about the value of the other variable.

what is correlation?

The correlation is a measure of the strength and direction of linear association between two quantitative variables.

what happens if a correlation is symmetric?

The correlation is symmetric: The correlation between variables x and y is the same as the correlation between y and x.

if correlation has no units that means?

The correlation r has no units and is independent of the scale of either variable.

what is correlation always between?

−1 and 1, inclusive:−1 ≤ r≤ 1.

the sign of r whether neg or pos show?

 The sign of r (positive or negative) indicates the direction of the association.

what shows a strong linear relationship?

Values of r close to +1 of−1 show a strong linear relationship.

what shows no linear relationship?

Values of r close to 0 show no linear relationship. However there may be a different kind of relationship.

what is true about correlations?

the correlation r means nothing if the relationship is not linear.

does correlation mean causation?

Correlation does NOT necessarily mean causation!!!!!

• ALWAYS plot your data AND take the context into account!!!!!