Standard: HSS.ID.B6c – Fit a linear function for a scatter plot that suggests a linear association.
Grade level: High School: Statistics & Probability
Subject: Mathematics
Domain: Interpreting Categorical & Quantitative Data
Teacher Overview
This standard focuses on fitting a linear function to a scatter plot that suggests a linear association. It’s crucial as it helps students understand how to model and interpret relationships between two quantitative variables, a foundational skill in statistics and data analysis. Students should be comfortable with plotting points on a graph, understanding basic linear equations, and recognizing patterns in data.
After mastering this standard, students will be able to use linear models to predict outcomes, understand the significance of the slope and intercept, and critically evaluate the appropriateness of linear models for different data sets.
Common Misconception 1
Some students might think that all scatter plots should show a perfect straight line. This is incorrect because real-world data often contains variability and noise, which means that even data with a linear trend will not form a perfect line.
Intervention 1
Use examples of real-world data sets that show a clear trend but also have variability. Discuss how the line of best fit represents the general trend rather than exact data points.
Common Misconception 2
Another common misconception is that the linear function should pass through all points in the scatter plot. This is not true because the line of best fit aims to minimize the overall distance from all points, not to pass through each one.
Intervention 2
Introduce the concept of least squares regression and demonstrate how the line of best fit is calculated to minimize the sum of squared distances from the points.
Prerequisite Knowledge
Students should understand basic concepts of scatter plots, linear equations, and correlation. They should also be familiar with plotting points on a graph and interpreting data trends.
Subsequent Knowledge
Students will learn to interpret the slope and intercept of a linear function in context, use linear models to make predictions, and understand the limitations of linear models in representing real-world data.
Instructional Activities
- Create scatter plots from given data sets and draw lines of best fit
- Analyze real-world data sets and discuss the linear relationships
- Use graphing calculators or software to fit linear functions to scatter plots
- Conduct experiments to collect data and analyze the linear associations
