Scatterplots

Scatterplots

• The quantitative variable that we are predicting is called the response variable, referred to as Y.
• Y is also known as the dependent variable.
• The quantitative variable that we are basing our predictions on is called the explanatory variable or predictor variable, referred to as X.
• X is also known as the independent variable.

• The number of transaction made at a store (X) explains the revenue generated (Y).
• The depth of a bathtub (X) determines how much water it could contain (Y).
• The number of hours spent at swim practice (X) predicts the time it takes to finish a lap (Y).

1. A positive (+) association,
2. A negative (−) association, or
3. No association

• Hours studied is the explanatory variable (X)
• Grade is the response variable (Y)

Important observations

1. The response variable (Y) is on the Y-axis; the explanatory (X) is on the X-axis.

• This is always the case, unless it is not obviously apparent (e.g. # incoming calls vs. # outgoing calls) in which case they can go in any axis.

1. The variables must be quantitative; we cannot make scatterplots based on categorical variables.
2. Each person $i$ is represented by a single data point in the scatterplot with an $\purple{(x_i,y_i)}$ coordinate.
3. The mean-mean point $(\overline{x},\overline{y})$ is always in the center of the cloud of data points.

• In this example, $(\overline{x},\overline{y})=(8.25,78.25)$