In this Grade 9 Saxon Algebra 1 lesson, students learn how to create scatter plots, draw trend lines, and identify positive correlation, negative correlation, or no correlation between two data sets. Students also practice finding the equation of a trend line using slope-intercept form and use a graphing calculator to calculate the line of best fit through linear regression. The lesson is part of Chapter 8 and builds on prior knowledge of slope and linear equations.
Section 1
📘 Making and Analyzing Scatter Plots
One type of graph that relates two sets of data with plotted ordered pairs is called a scatter plot.
Next, you’ll learn to draw trend lines on these plots to analyze the strength and direction of these relationships.
Section 2
Scatter plot
One type of graph that relates two sets of data with plotted ordered pairs is called a scatter plot. Scatter plots are considered discrete graphs because their points are separate and disconnected.
Think of a scatter plot as a data detective's corkboard! Each point is a clue showing how two things, like study time and test scores, might be connected. We're looking for a pattern by seeing how the dots are scattered across the graph, which helps us understand their relationship.
Plotting points for (hours of sunshine, flowers in bloom) to see if more sun means more flowers.
A graph showing individual student's data for (time spent on video games, grade in science class).
Tracking points for (age of a phone, its battery life) to observe if there's a downward trend.
Section 3
Trend line
A trend line is a line on a scatter plot, which shows the relationship between two sets of data. It does not have to go through any of the points on the scatter plot.
A trend line is the 'best guess' straight path through your scattered data points. It doesn’t have to hit any dots, but it reveals the general direction—uphill for positive or downhill for negative—that your data is heading. It’s a quick visual summary of the relationship between your variables.
For points (1, 5), (2, 7), (3, 6), and (4, 9), a trend line would be a straight line rising from left to right.
A trend line with a positive slope like indicates a positive correlation.
A trend line with a negative slope like indicates a negative correlation.
Section 4
Example Card: Graphing a Scatter Plot and Trend Line
Let's turn a simple table of numbers into a visual story and find the line that tells its tale. This example uses the key idea of creating a scatter plot and a trend line.
Example Problem: Make a scatter plot, draw a trend line, and find its equation for this data:
| x | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| y | 5 | 9 | 12 | 17 | 20 | 25 |
Section 5
Line of best fit
A trend line that shows the linear relationship of a scatter plot the most accurately is called the line of best fit. It is also referred to as the regression line.
While any trend line is a good guess, the line of best fit is the VIP—a mathematically perfect line that gets as close as possible to all data points. It provides the most accurate summary of a trend, giving you a powerful equation like for making predictions.
A calculator might find the equation as the line of best fit for homework and test grades.
Using an equation like to predict the US population for a future year.
This line is more precise than a hand-drawn trend line because it is calculated, not just visually estimated.
Section 6
Example Card: Calculating a Line of Best Fit
A hand-drawn line is a good estimate, but a calculator can find the perfect line of best fit with precision. This example focuses on the key idea of using a tool to calculate the line of best fit.
Example Problem: Find the equation for the line of best fit for the data on hours studied versus exam scores for eight students.
Hours Studied vs. Exam Score
| Hours Studied | 2 | 3 | 5 | 5.5 | 6 | 7 | 8 | 9.5 |
|---|---|---|---|---|---|---|---|---|
| Exam Score | 65 | 70 | 78 | 85 | 82 | 90 | 94 | 98 |
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Section 1
📘 Making and Analyzing Scatter Plots
One type of graph that relates two sets of data with plotted ordered pairs is called a scatter plot.
Next, you’ll learn to draw trend lines on these plots to analyze the strength and direction of these relationships.
Section 2
Scatter plot
One type of graph that relates two sets of data with plotted ordered pairs is called a scatter plot. Scatter plots are considered discrete graphs because their points are separate and disconnected.
Think of a scatter plot as a data detective's corkboard! Each point is a clue showing how two things, like study time and test scores, might be connected. We're looking for a pattern by seeing how the dots are scattered across the graph, which helps us understand their relationship.
Plotting points for (hours of sunshine, flowers in bloom) to see if more sun means more flowers.
A graph showing individual student's data for (time spent on video games, grade in science class).
Tracking points for (age of a phone, its battery life) to observe if there's a downward trend.
Section 3
Trend line
A trend line is a line on a scatter plot, which shows the relationship between two sets of data. It does not have to go through any of the points on the scatter plot.
A trend line is the 'best guess' straight path through your scattered data points. It doesn’t have to hit any dots, but it reveals the general direction—uphill for positive or downhill for negative—that your data is heading. It’s a quick visual summary of the relationship between your variables.
For points (1, 5), (2, 7), (3, 6), and (4, 9), a trend line would be a straight line rising from left to right.
A trend line with a positive slope like indicates a positive correlation.
A trend line with a negative slope like indicates a negative correlation.
Section 4
Example Card: Graphing a Scatter Plot and Trend Line
Let's turn a simple table of numbers into a visual story and find the line that tells its tale. This example uses the key idea of creating a scatter plot and a trend line.
Example Problem: Make a scatter plot, draw a trend line, and find its equation for this data:
| x | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| y | 5 | 9 | 12 | 17 | 20 | 25 |
Section 5
Line of best fit
A trend line that shows the linear relationship of a scatter plot the most accurately is called the line of best fit. It is also referred to as the regression line.
While any trend line is a good guess, the line of best fit is the VIP—a mathematically perfect line that gets as close as possible to all data points. It provides the most accurate summary of a trend, giving you a powerful equation like for making predictions.
A calculator might find the equation as the line of best fit for homework and test grades.
Using an equation like to predict the US population for a future year.
This line is more precise than a hand-drawn trend line because it is calculated, not just visually estimated.
Section 6
Example Card: Calculating a Line of Best Fit
A hand-drawn line is a good estimate, but a calculator can find the perfect line of best fit with precision. This example focuses on the key idea of using a tool to calculate the line of best fit.
Example Problem: Find the equation for the line of best fit for the data on hours studied versus exam scores for eight students.
Hours Studied vs. Exam Score
| Hours Studied | 2 | 3 | 5 | 5.5 | 6 | 7 | 8 | 9.5 |
|---|---|---|---|---|---|---|---|---|
| Exam Score | 65 | 70 | 78 | 85 | 82 | 90 | 94 | 98 |
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter