Scatterplots Lecture 18 Sec. 4.4.6 Fri, Oct 1, 2004

Bivariate Data Bivariate data – For each unit in the sample, two measurements are taken, i.e., two variables are measured.

Response and Explanatory Variables Many studies attempt to find a relationship between two separate quantities. The response variable measures a characteristic of interest. The explanatory variable is a potential explanation of the response variable. That is, variations in the response variable are “explained” by variations in the explanatory variable.

Example For example, taller people tend to weigh more and shorter people tend to weigh less. Which is the response variable? Height or weight? Which is the explanatory variable?

Response and Explanatory Variables The explanatory variable is also called the independent variable. It is denoted x. The response variable is also called the dependent variable. The response “depends” on the value of x. The response is denoted y.

Let’s Do It! Let’s do it! 4.19, p. 237 – Possible Explanations.

Scatterplots Scatterplot – A display of bivariate quantitative data that shows the relationship between the response variable and the explanatory variable. The horizontal axis represents the explanatory variable. The vertical axis represents the response variable.

Let’s Do It! Let’s do it! 4.20, p. 238 – Some Data Points. The Excel spreadsheet. Draw the trend line.

Interpreting Scatterplots What characteristics do we look for in the relationship? As the explanatory variable increases, does the response variable Increase? Decrease? Remain constant? None of the above?

Interpreting Scatterplots If the response variable tends to increase as the explanatory increases, then the variables are positively associated. If the response variable tends to decrease as the explanatory increases, then the variables are negatively associated.

Interpreting Scatterplots Suppose the response variable tends to decrease as the explanatory variable decreases. Is that a positive association or a negative association?

Interpreting Scatterplots If there is an association, is it strong, moderate, or weak? It is strong if the points are tightly clustered along a line. It is moderate if the points are loosely clustered along a line. It is weak if there is little or no clustering.

Let’s Do It! Let’s do it! 4.21, p. 240 – What Direction? Let’s do it! 4.22, p. 240 – Oil-Change Data. The Excel spreadsheet. Let’s do it! 4.23, p. 241 – Right versus Left.