STATS Chapter 4: Scatterplots and Correlation

Facts About Correlation

1. Correlation makes no distinction between explanatory and response variables. 2. r has no units and does not change when we change the units of measurement of x, y, or both. 3. Positive r indicates positive association between the variables, and negative r indicates negative association. 4. The correlation r is always a number between -1 and 1.

How to Make a Scatterplot

1. Decide which variable should go on each axis. If a distinction exists, plot the explanatory variable on the x-axis and the response variable on the y-axis. 2. Label and scale your axes. 3. Plot individual data values.

How to Examine a Scatterplot

As in any graph of data, look for the overall pattern and for striking departures from that pattern. You can describe the overall pattern of a scatterplot by the direction, form, and strength of the relationship. An important kind of departure is an outlier, an individual value that falls outside the overall pattern of the relationship.

Linear relationship?

Correlation is close to zero. The greater the digit of slope, the tighter the scatter plot

Curved relationship

Correlation is misleading.

predictor variable

a variable that can be used to predict the value of another variable (as in statistical regression)

Two variables have a positive association when

above-average values of one tend to accompany above-average values of the other, and when below-average values also tend to occur together.

Two variables have a negative association when

above-average values of one tend to accompany below-average values of the other.

explanatory variable

may help explain or influence changes in a response variable.

response variable

measures an outcome of a study.

The correlation r measures the strength of the linear relationship between two quantitative variables.

r is always a number between -1 and 1. r > 0 indicates a positive association. r < 0 indicates a negative association. Values of r near 0 indicate a very weak linear relationship. The strength of the linear relationship increases as r moves away from 0 toward -1 or 1. The extreme values r = -1 and r = 1 occur only in the case of a perfect linear relationship.

The most useful graph for displaying the relationship between two quantitative variables is a scatterplot. What does it do?

shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph. A scatterplot displays the strength, direction, and form of the relationship between two quantitative variables.