Line Of Best Fit (Least Square Method) - Varsity Tutors

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Line of Best Fit (Least Square Method)

Study Guide

Key Definition

A line of best fit is a straight line that best represents the data on a scatter plot. It can be found using the least square method to minimize the distance between the line and all of the data points.

Important Notes

  • The line of best fit is used to study the relationship between two variables.
  • A rough line of best fit can be drawn by eyeballing the graph.
  • The least square method provides a precise equation for the line.
  • The least squares line does not necessarily split the data into equal counts above and below.
  • Avoid major errors in identifying the x-intercept and y-intercept.

Mathematical Notation

$y = mx + b$ is the equation of a line$\sum$ represents summation$x^2$ is x squaredRemember to use proper notation when solving problems

Why It Works

The least square method minimizes the sum of the squares of the vertical distances of the points from the line. This ensures the best fit for the data.

Remember

To find the line of best fit, ensure your line minimizes the sum of squared differences from each point to the line.

Quick Reference

Equation of Line:$y = mx + b$Sum of Squares:$\sum (y_i - (mx_i + b))^2$

Understanding Line of Best Fit (Least Square Method)

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Video explanation of this concept

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Beginner Explanation

A simple explanation is that the line of best fit is the line that best summarizes the trend of the data points. It minimizes the error between the data points and the line.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Which of the following equations represents a line of best fit? $y = mx + b$

A$y = 2x + 3$B$y = x^2 + 3$C$y = \sqrt{x} + 3$D$y = \frac{1}{x} + 3$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

Imagine you are analyzing your weekly allowance compared to your chores completed. You want to determine the relationship using a line of best fit.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Consider how the line of best fit might change if outliers are present. Describe the impact of outliers on the line.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Given the data set, what is the equation for the line of best fit using the least square method?

A$y = 0.5x + 1.2$B$y = 0.8x - 0.4$C$y = 1.2x + 0.5$D$y = -0.5x + 2.4$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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