Lesson 5: Scatter Plots and Lines of Fit

Property

A scatter plot is a graph that displays data as points plotted on a coordinate plane, where each point represents a pair of values $(x, y)$.
Scatter plots help visualize the relationship between two variables and show whether there is a pattern or trend in the data.

Examples

Property

Positive Association: As $x$-values increase, $y$-values tend to increase (upward trend)

Negative Association: As $x$-values increase, $y$-values tend to decrease (downward trend)

Property

Association describes the general relationship pattern between two variables (positive, negative, or no association), while correlation specifically refers to linear relationships that can be modeled with a straight line equation of the form $y = mx + b$.

Examples

Property

A trend line (or line of best fit/regression line) is a straight line drawn on a scatter plot that models the relationship between two quantitative variables. It provides a one-dimensional summary of a bivariate (2-dimensional) data set by showing the general direction of the data.

To draw it, use the primary method of 'eye-balling' to find the line that minimizes the distance between each data point and that line. A line of best fit will have about the same number of points above and below it and may or may not pass through any of the data points.

Examples

• If the number of hours studied increases and test scores also tend to increase, a trend line would have a positive slope, showing a positive association.
• A scatter plot shows hours spent practicing piano versus number of mistakes made in a performance. The points trend downwards, so an 'eyeballed' line with a negative slope is drawn to show that more practice is associated with fewer mistakes.
• Data is collected on daily temperature and the number of bottles of water sold at a park. The points on the scatter plot go up and to the right. An 'eyeballed' line with a positive slope summarizes this positive association.