Illustrative Math Alignment: Grade 8 Unit 3
Linear Relationships
Lesson 11: Equations of All Kinds of Lines
Use the following Media4Math resources with this Illustrative Math lesson.
| Thumbnail Image | Title | Body | Curriculum Topic |
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Video Definition 18--Linear Function Concepts--Line of Best Fit | Video Definition 18--Linear Function Concepts--Line of Best Fit
TopicLinear Functions DescriptionThe term is "Line of Best Fit," defined as a linear function that serves as a model for a set of scatterplot data. It helps represent the central trend of data points. This term enhances understanding of linear functions in the context of data analysis and graphical trends. |
Graphs of Linear Functions |
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Video Definition 18--Linear Function Concepts--Line of Best Fit | Video Definition 18--Linear Function Concepts--Line of Best Fit
TopicLinear Functions DescriptionThe term is "Line of Best Fit," defined as a linear function that serves as a model for a set of scatterplot data. It helps represent the central trend of data points. This term enhances understanding of linear functions in the context of data analysis and graphical trends. |
Graphs of Linear Functions |
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Video Definition 19--Linear Function Concepts--Slope | Video Definition 19--Linear Function Concepts--Slope
TopicLinear Functions DescriptionThe term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction. |
Slope |
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Video Definition 19--Linear Function Concepts--Slope | Video Definition 19--Linear Function Concepts--Slope
TopicLinear Functions DescriptionThe term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction. |
Slope |
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Video Definition 19--Linear Function Concepts--Slope | Video Definition 19--Linear Function Concepts--Slope
TopicLinear Functions DescriptionThe term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction. |
Slope |
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Video Definition 19--Linear Function Concepts--Slope | Video Definition 19--Linear Function Concepts--Slope
TopicLinear Functions DescriptionThe term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction. |
Slope |
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Video Definition 19--Linear Function Concepts--Slope | Video Definition 19--Linear Function Concepts--Slope
TopicLinear Functions DescriptionThe term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction. |
Slope |
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Video Definition 19--Linear Function Concepts--Slope | Video Definition 19--Linear Function Concepts--Slope
TopicLinear Functions DescriptionThe term is "Slope of a Line," defined as the ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance. Represented as m in the equation y = mx + b. This term is a fundamental component of linear equations, providing a measure of steepness and direction. |
Slope |
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Video Definition 2--Linear Function Concepts--Constant Function | Video Definition 2--Linear Function Concepts--Constant Function
TopicLinear Functions DescriptionThe term is "Constant Function," defined as a linear function of the form y = b, where b is the y-intercept. The graph of a constant function is horizontal with a slope of m = 0. An example graph is shown with a horizontal line at y = b. This term demonstrates a special case of linear functions, emphasizing the role of constant values and their graphical representation as horizontal lines. |
Slope-Intercept Form |
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Video Definition 2--Linear Function Concepts--Constant Function | Video Definition 2--Linear Function Concepts--Constant Function
TopicLinear Functions DescriptionThe term is "Constant Function," defined as a linear function of the form y = b, where b is the y-intercept. The graph of a constant function is horizontal with a slope of m = 0. An example graph is shown with a horizontal line at y = b. This term demonstrates a special case of linear functions, emphasizing the role of constant values and their graphical representation as horizontal lines. |
Slope-Intercept Form |
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Video Definition 2--Linear Function Concepts--Constant Function | Video Definition 2--Linear Function Concepts--Constant Function
TopicLinear Functions DescriptionThe term is "Constant Function," defined as a linear function of the form y = b, where b is the y-intercept. The graph of a constant function is horizontal with a slope of m = 0. An example graph is shown with a horizontal line at y = b. This term demonstrates a special case of linear functions, emphasizing the role of constant values and their graphical representation as horizontal lines. |
Slope-Intercept Form |
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Video Definition 2--Linear Function Concepts--Constant Function | Video Definition 2--Linear Function Concepts--Constant Function
TopicLinear Functions DescriptionThe term is "Constant Function," defined as a linear function of the form y = b, where b is the y-intercept. The graph of a constant function is horizontal with a slope of m = 0. An example graph is shown with a horizontal line at y = b. This term demonstrates a special case of linear functions, emphasizing the role of constant values and their graphical representation as horizontal lines. |
Slope-Intercept Form |
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Video Definition 2--Linear Function Concepts--Constant Function | Video Definition 2--Linear Function Concepts--Constant Function
TopicLinear Functions DescriptionThe term is "Constant Function," defined as a linear function of the form y = b, where b is the y-intercept. The graph of a constant function is horizontal with a slope of m = 0. An example graph is shown with a horizontal line at y = b. This term demonstrates a special case of linear functions, emphasizing the role of constant values and their graphical representation as horizontal lines. |
Slope-Intercept Form |
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Video Definition 2--Linear Function Concepts--Constant Function | Video Definition 2--Linear Function Concepts--Constant Function
TopicLinear Functions DescriptionThe term is "Constant Function," defined as a linear function of the form y = b, where b is the y-intercept. The graph of a constant function is horizontal with a slope of m = 0. An example graph is shown with a horizontal line at y = b. This term demonstrates a special case of linear functions, emphasizing the role of constant values and their graphical representation as horizontal lines. |
Slope-Intercept Form |
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Video Definition 20--Linear Function Concepts--System of Linear Equations | Video Definition 20--Linear Function Concepts--System of Linear Equations
TopicLinear Functions DescriptionThe term is "System of Linear Equations," defined as a collection of linear equations where the number of equations matches the number of variables, allowing for an algebraic solution. Examples include 2-variable and 3-variable systems. This term introduces the concept of interacting linear equations, paving the way for multi-variable problem-solving. |
Applications of Linear Functions and Graphs of Linear Functions |
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Video Definition 20--Linear Function Concepts--System of Linear Equations | Video Definition 20--Linear Function Concepts--System of Linear Equations
TopicLinear Functions DescriptionThe term is "System of Linear Equations," defined as a collection of linear equations where the number of equations matches the number of variables, allowing for an algebraic solution. Examples include 2-variable and 3-variable systems. This term introduces the concept of interacting linear equations, paving the way for multi-variable problem-solving. |
Applications of Linear Functions and Graphs of Linear Functions |
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Video Definition 20--Linear Function Concepts--System of Linear Equations | Video Definition 20--Linear Function Concepts--System of Linear Equations
TopicLinear Functions DescriptionThe term is "System of Linear Equations," defined as a collection of linear equations where the number of equations matches the number of variables, allowing for an algebraic solution. Examples include 2-variable and 3-variable systems. This term introduces the concept of interacting linear equations, paving the way for multi-variable problem-solving. |
Applications of Linear Functions and Graphs of Linear Functions |
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Video Definition 20--Linear Function Concepts--System of Linear Equations | Video Definition 20--Linear Function Concepts--System of Linear Equations
TopicLinear Functions DescriptionThe term is "System of Linear Equations," defined as a collection of linear equations where the number of equations matches the number of variables, allowing for an algebraic solution. Examples include 2-variable and 3-variable systems. This term introduces the concept of interacting linear equations, paving the way for multi-variable problem-solving. |
Applications of Linear Functions and Graphs of Linear Functions |
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Video Definition 20--Linear Function Concepts--System of Linear Equations | Video Definition 20--Linear Function Concepts--System of Linear Equations
TopicLinear Functions DescriptionThe term is "System of Linear Equations," defined as a collection of linear equations where the number of equations matches the number of variables, allowing for an algebraic solution. Examples include 2-variable and 3-variable systems. This term introduces the concept of interacting linear equations, paving the way for multi-variable problem-solving. |
Applications of Linear Functions and Graphs of Linear Functions |
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Video Definition 20--Linear Function Concepts--System of Linear Equations | Video Definition 20--Linear Function Concepts--System of Linear Equations
TopicLinear Functions DescriptionThe term is "System of Linear Equations," defined as a collection of linear equations where the number of equations matches the number of variables, allowing for an algebraic solution. Examples include 2-variable and 3-variable systems. This term introduces the concept of interacting linear equations, paving the way for multi-variable problem-solving. |
Applications of Linear Functions and Graphs of Linear Functions |
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Video Definition 21--Linear Function Concepts--Solution to a Linear Equation | Video Definition 21--Linear Function Concepts--Solution to a Linear Equation
TopicLinear Functions DescriptionThe term is "Solution to a Linear Equation," defined as finding the value(s) of a variable that make the equation true. An example includes solving 2x + 5 = 15 step-by-step to find x = 5. This term explains how linear equations are solved, demonstrating the logical process of isolating variables. |
Solving Systems of Equations |
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Video Definition 21--Linear Function Concepts--Solution to a Linear Equation | Video Definition 21--Linear Function Concepts--Solution to a Linear Equation
TopicLinear Functions DescriptionThe term is "Solution to a Linear Equation," defined as finding the value(s) of a variable that make the equation true. An example includes solving 2x + 5 = 15 step-by-step to find x = 5. This term explains how linear equations are solved, demonstrating the logical process of isolating variables. |
Solving Systems of Equations |
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Video Definition 21--Linear Function Concepts--Solution to a Linear Equation | Video Definition 21--Linear Function Concepts--Solution to a Linear Equation
TopicLinear Functions DescriptionThe term is "Solution to a Linear Equation," defined as finding the value(s) of a variable that make the equation true. An example includes solving 2x + 5 = 15 step-by-step to find x = 5. This term explains how linear equations are solved, demonstrating the logical process of isolating variables. |
Solving Systems of Equations |
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Video Definition 21--Linear Function Concepts--Solution to a Linear Equation | Video Definition 21--Linear Function Concepts--Solution to a Linear Equation
TopicLinear Functions DescriptionThe term is "Solution to a Linear Equation," defined as finding the value(s) of a variable that make the equation true. An example includes solving 2x + 5 = 15 step-by-step to find x = 5. This term explains how linear equations are solved, demonstrating the logical process of isolating variables. |
Solving Systems of Equations |
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Video Definition 21--Linear Function Concepts--Solution to a Linear Equation | Video Definition 21--Linear Function Concepts--Solution to a Linear Equation
TopicLinear Functions DescriptionThe term is "Solution to a Linear Equation," defined as finding the value(s) of a variable that make the equation true. An example includes solving 2x + 5 = 15 step-by-step to find x = 5. This term explains how linear equations are solved, demonstrating the logical process of isolating variables. |
Solving Systems of Equations |
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Video Definition 21--Linear Function Concepts--Solution to a Linear Equation | Video Definition 21--Linear Function Concepts--Solution to a Linear Equation
TopicLinear Functions DescriptionThe term is "Solution to a Linear Equation," defined as finding the value(s) of a variable that make the equation true. An example includes solving 2x + 5 = 15 step-by-step to find x = 5. This term explains how linear equations are solved, demonstrating the logical process of isolating variables. |
Solving Systems of Equations |
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Video Definition 22--Linear Function Concepts--Proportional Relationship | Video Definition 22--Linear Function Concepts--Proportional Relationship
TopicLinear Functions DescriptionThe term is "Proportional Relationship," defined as a type of linear relationship where two variables maintain a constant ratio. Represented as y = kx, where k is the constant ratio. This term establishes the foundation for understanding direct variation and proportionality in linear relationships. |
Proportions |
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Video Definition 22--Linear Function Concepts--Proportional Relationship | Video Definition 22--Linear Function Concepts--Proportional Relationship
TopicLinear Functions DescriptionThe term is "Proportional Relationship," defined as a type of linear relationship where two variables maintain a constant ratio. Represented as y = kx, where k is the constant ratio. This term establishes the foundation for understanding direct variation and proportionality in linear relationships. |
Proportions |
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Video Definition 22--Linear Function Concepts--Proportional Relationship | Video Definition 22--Linear Function Concepts--Proportional Relationship
TopicLinear Functions DescriptionThe term is "Proportional Relationship," defined as a type of linear relationship where two variables maintain a constant ratio. Represented as y = kx, where k is the constant ratio. This term establishes the foundation for understanding direct variation and proportionality in linear relationships. |
Proportions |
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Video Definition 22--Linear Function Concepts--Proportional Relationship | Video Definition 22--Linear Function Concepts--Proportional Relationship
TopicLinear Functions DescriptionThe term is "Proportional Relationship," defined as a type of linear relationship where two variables maintain a constant ratio. Represented as y = kx, where k is the constant ratio. This term establishes the foundation for understanding direct variation and proportionality in linear relationships. |
Proportions |
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Video Definition 22--Linear Function Concepts--Proportional Relationship | Video Definition 22--Linear Function Concepts--Proportional Relationship
TopicLinear Functions DescriptionThe term is "Proportional Relationship," defined as a type of linear relationship where two variables maintain a constant ratio. Represented as y = kx, where k is the constant ratio. This term establishes the foundation for understanding direct variation and proportionality in linear relationships. |
Proportions |
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Video Definition 22--Linear Function Concepts--Proportional Relationship | Video Definition 22--Linear Function Concepts--Proportional Relationship
TopicLinear Functions DescriptionThe term is "Proportional Relationship," defined as a type of linear relationship where two variables maintain a constant ratio. Represented as y = kx, where k is the constant ratio. This term establishes the foundation for understanding direct variation and proportionality in linear relationships. |
Proportions |
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Video Definition 23--Linear Function Concepts--Scatter Plot | Video Definition 23--Linear Function Concepts--Scatter Plot
TopicLinear Functions DescriptionThe term is "Scatter Plot," defined as a graph displaying individual data points as dots, where each dot represents the values of two variables. Used to examine relationships and identify patterns or trends. This term provides a graphical tool to visualize and analyze linear relationships in data. |
Data Analysis |
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Video Definition 23--Linear Function Concepts--Scatter Plot | Video Definition 23--Linear Function Concepts--Scatter Plot
TopicLinear Functions DescriptionThe term is "Scatter Plot," defined as a graph displaying individual data points as dots, where each dot represents the values of two variables. Used to examine relationships and identify patterns or trends. This term provides a graphical tool to visualize and analyze linear relationships in data. |
Data Analysis |
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Video Definition 23--Linear Function Concepts--Scatter Plot | Video Definition 23--Linear Function Concepts--Scatter Plot
TopicLinear Functions DescriptionThe term is "Scatter Plot," defined as a graph displaying individual data points as dots, where each dot represents the values of two variables. Used to examine relationships and identify patterns or trends. This term provides a graphical tool to visualize and analyze linear relationships in data. |
Data Analysis |
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Video Definition 23--Linear Function Concepts--Scatter Plot | Video Definition 23--Linear Function Concepts--Scatter Plot
TopicLinear Functions DescriptionThe term is "Scatter Plot," defined as a graph displaying individual data points as dots, where each dot represents the values of two variables. Used to examine relationships and identify patterns or trends. This term provides a graphical tool to visualize and analyze linear relationships in data. |
Data Analysis |
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Video Definition 23--Linear Function Concepts--Scatter Plot | Video Definition 23--Linear Function Concepts--Scatter Plot
TopicLinear Functions DescriptionThe term is "Scatter Plot," defined as a graph displaying individual data points as dots, where each dot represents the values of two variables. Used to examine relationships and identify patterns or trends. This term provides a graphical tool to visualize and analyze linear relationships in data. |
Data Analysis |
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Video Definition 23--Linear Function Concepts--Scatter Plot | Video Definition 23--Linear Function Concepts--Scatter Plot
TopicLinear Functions DescriptionThe term is "Scatter Plot," defined as a graph displaying individual data points as dots, where each dot represents the values of two variables. Used to examine relationships and identify patterns or trends. This term provides a graphical tool to visualize and analyze linear relationships in data. |
Data Analysis |
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Video Definition 24--Linear Function Concepts--Least Squares Regression Line | Video Definition 24--Linear Function Concepts--Least Squares Regression Line
TopicLinear Functions DescriptionThe term is "Least Squares Regression Line," defined as the best fit to a set of data points on a scatter plot. It minimizes the sum of the squares of the vertical distances between the data points and the line. This term links linear functions to data analysis, providing a method to model relationships in data. |
Data Analysis |
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Video Definition 24--Linear Function Concepts--Least Squares Regression Line | Video Definition 24--Linear Function Concepts--Least Squares Regression Line
TopicLinear Functions DescriptionThe term is "Least Squares Regression Line," defined as the best fit to a set of data points on a scatter plot. It minimizes the sum of the squares of the vertical distances between the data points and the line. This term links linear functions to data analysis, providing a method to model relationships in data. |
Data Analysis |
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Video Definition 24--Linear Function Concepts--Least Squares Regression Line | Video Definition 24--Linear Function Concepts--Least Squares Regression Line
TopicLinear Functions DescriptionThe term is "Least Squares Regression Line," defined as the best fit to a set of data points on a scatter plot. It minimizes the sum of the squares of the vertical distances between the data points and the line. This term links linear functions to data analysis, providing a method to model relationships in data. |
Data Analysis |
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Video Definition 24--Linear Function Concepts--Least Squares Regression Line | Video Definition 24--Linear Function Concepts--Least Squares Regression Line
TopicLinear Functions DescriptionThe term is "Least Squares Regression Line," defined as the best fit to a set of data points on a scatter plot. It minimizes the sum of the squares of the vertical distances between the data points and the line. This term links linear functions to data analysis, providing a method to model relationships in data. |
Data Analysis |
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Video Definition 24--Linear Function Concepts--Least Squares Regression Line | Video Definition 24--Linear Function Concepts--Least Squares Regression Line
TopicLinear Functions DescriptionThe term is "Least Squares Regression Line," defined as the best fit to a set of data points on a scatter plot. It minimizes the sum of the squares of the vertical distances between the data points and the line. This term links linear functions to data analysis, providing a method to model relationships in data. |
Data Analysis |
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Video Definition 24--Linear Function Concepts--Least Squares Regression Line | Video Definition 24--Linear Function Concepts--Least Squares Regression Line
TopicLinear Functions DescriptionThe term is "Least Squares Regression Line," defined as the best fit to a set of data points on a scatter plot. It minimizes the sum of the squares of the vertical distances between the data points and the line. This term links linear functions to data analysis, providing a method to model relationships in data. |
Data Analysis |
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Video Definition 25--Linear Function Concepts--Linear Regression | Video Definition 25--Linear Function Concepts--Linear Regression
TopicLinear Functions DescriptionThe term is "Linear Regression," defined as a statistical method used to analyze the relationship between two variables by fitting a linear equation to observed data points. An example includes using LinReg to calculate slope (m), intercept (b), and r-squared values. This term links linear functions with statistical applications, particularly in modeling and predictions based on data. |
Data Analysis |
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Video Definition 25--Linear Function Concepts--Linear Regression | Video Definition 25--Linear Function Concepts--Linear Regression
TopicLinear Functions DescriptionThe term is "Linear Regression," defined as a statistical method used to analyze the relationship between two variables by fitting a linear equation to observed data points. An example includes using LinReg to calculate slope (m), intercept (b), and r-squared values. This term links linear functions with statistical applications, particularly in modeling and predictions based on data. |
Data Analysis |
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Video Definition 25--Linear Function Concepts--Linear Regression | Video Definition 25--Linear Function Concepts--Linear Regression
TopicLinear Functions DescriptionThe term is "Linear Regression," defined as a statistical method used to analyze the relationship between two variables by fitting a linear equation to observed data points. An example includes using LinReg to calculate slope (m), intercept (b), and r-squared values. This term links linear functions with statistical applications, particularly in modeling and predictions based on data. |
Data Analysis |
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Video Definition 25--Linear Function Concepts--Linear Regression | Video Definition 25--Linear Function Concepts--Linear Regression
TopicLinear Functions DescriptionThe term is "Linear Regression," defined as a statistical method used to analyze the relationship between two variables by fitting a linear equation to observed data points. An example includes using LinReg to calculate slope (m), intercept (b), and r-squared values. This term links linear functions with statistical applications, particularly in modeling and predictions based on data. |
Data Analysis |
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Video Definition 25--Linear Function Concepts--Linear Regression | Video Definition 25--Linear Function Concepts--Linear Regression
TopicLinear Functions DescriptionThe term is "Linear Regression," defined as a statistical method used to analyze the relationship between two variables by fitting a linear equation to observed data points. An example includes using LinReg to calculate slope (m), intercept (b), and r-squared values. This term links linear functions with statistical applications, particularly in modeling and predictions based on data. |
Data Analysis |
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Video Definition 25--Linear Function Concepts--Linear Regression | Video Definition 25--Linear Function Concepts--Linear Regression
TopicLinear Functions DescriptionThe term is "Linear Regression," defined as a statistical method used to analyze the relationship between two variables by fitting a linear equation to observed data points. An example includes using LinReg to calculate slope (m), intercept (b), and r-squared values. This term links linear functions with statistical applications, particularly in modeling and predictions based on data. |
Data Analysis |
