Math - 2019-20
8.13 - Scatterplots
8.13 The student will
a) represent data in scatterplots;
b) make observations about data represented in scatterplots;
c) use a drawing to estimate the line of best fit for data represented in a scatterplot.
- I can determine if there is a correlation between number of
study hours and test scores, predict how much my cell phone bill will be, and decide
if I need to worry about global warming.
- I will realize that real-life data often
follows a linear pattern which provides easy predictions.
UNDERSTANDING THE STANDARD
· A scatterplot illustrates the relationship between two sets of numerical data represented by two variables (bivariate data). A scatterplot consists of points on the coordinate plane. The coordinates of the point represent the measures of the two attributes of the point.
· In a scatterplot, each point may represent an independent and dependent variable. The independent variable is graphed on the horizontal axis and the dependent is graphed on the vertical axis.
· Scatterplots can be used to predict linear trends and estimate a line of best fit.
· A line of best fit helps in making interpretations and predictions about the situation modeled in the data set. Lines and curves of best fit are explored more in Algebra I to make interpretations and predictions.
· A scatterplot can suggest various kinds of linear relationships between variables. For example, weight and height, where weight would be on y-axis and height would be on the x-axis. Linear relationships may be positive (rising) or negative (falling). If the pattern of points slopes from lower left to upper right, it indicates a positive linear relationship between the variables being studied. If the pattern of points slopes from upper left to lower right, it indicates a negative linear relationship.
- For example: The following scatterplots illustrate how patterns in data values may indicate linear relationships.
No relationship Positive relationship Negative relationship
· A linear relationship between variables does not necessarily imply causation. For example, as the temperature at the beach increases, the sales at an ice cream store increase. If data were collected for these two variables, a positive linear relationship would exist, however, there is no causal relationship between the variables (i.e., the temperature outside does not cause ice cream sales to increase, but there is a relationship between the two).· The relationship between variables is not always linear, and may be modeled by other types of functions that are studied in high school and college level mathematics.
- Why do we
estimate a line of best fit for a scatterplot?
A line of best fit helps in making interpretations and predictions about the situation modeled in the data set.
- What are the
inferences that can be drawn from sets of data points having a positive
relationship, a negative relationship, and no relationship?
Sets of data points with positive relationships demonstrate that the values of the two variables are increasing. A negative relationship indicates that as the value of the independent variable increases, the value of the dependent variable decreases.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
organize, and represent a data set of no more than 20 items using scatterplots.
· 8.13c1 Estimate the line of best fit with a drawing for data represented in a scatterplot.
· 8.13b1 Make observations about a set of data points in a scatterplot as having a positive linear relationship, a negative linear relationship, or no relationship.