Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
Math.8.SP.2 or 8.SP.A.2
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
Math.8.SP.3 or 8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
Math.8.SP.4 or 8.SP.A.4
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
Scatter plots are often used to see if an association, or correlation, exists between two variables. If the data points are clustered about a line or curve, they have a linear or nonlinear association, respectively. If the values on the vertical axis tend to increase as the values on the horizontal axis increase, then the data points have a positive association. If the values on the vertical axis tend to decrease as the values on the horizontal axis increase, then the data points have a negative association. If the values on the vertical axis vary as the values on the horizontal axis increase, then the data points have no association. If an association exists, with the exception of one, or some, data points, those points are referred to as outliers.
positive, linear association
negative, linear association
has an outlier at (4, 10)
If a linear association exists, an equation can be developed to model the relationship. The equation can be used to make predictions about the data. The equation is derived from a straight line drawn to fit the data. This line is referred to as a trend line, line of best fit, and/or regression line. Fitting the line to the data does not necessarily mean the line contains as many data points as possible. The line can go through all, some, or none of the data points. The line should be drawn such that it best represents the trend of the data. On the scatter plots below, the line on the left is a better trend line than the one on the right.