Scatterplots Lecture 19 Sec. 4.4.6 Wed, Feb 18, 2004

Response and Explanatory Variables Many studies attempt to find a relationship between two separate quantities. For each unit in the sample, two measurements are taken. One for the explanatory variable (x). One for the response variable (y). The response variable measures the characteristic of interest.

Response and Explanatory Variables 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. The response variable is also called the dependent variable. The response “depends” on the other variable.

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 (x-axis) represents the explanatory variable. The vertical axis (y-axis) represents the response variable.

Let’s Do It! Let’s do it! 4.20, p. 238 – Some Data Points.

Trend Lines In fact, Excel will 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?

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 diagonal line. It is moderate if the points are loosely clustered along a diagonal line. It is weak if there is very little clustering along any line.

Homework vs. Test

Homework vs. Test

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. Let’s do it! 4.23, p. 241 – Right versus Left.

Let’s Do It!

Assignment Page 243: Exercises 45 – 54. Page 249: Exercises 74 – 76.