9.2A- Linear Regression Regression Line = Line of best fit The line for which the sum of the squares of the residuals is a minimum Residuals (d) = distance.

Slides:

Advertisements

Similar presentations

R Squared. r = r = -.79 y = x y = x if x = 15, y = ? y = (15) y = if x = 6, y = ? y = (6)

Advertisements

Correlation and Regression

Definition  Regression Model  Regression Equation Y i =  0 +  1 X i ^ Given a collection of paired data, the regression equation algebraically describes.

Bellwork  Rewrite in slope intercept form:  4x + 2y = 8  3x = 4 – 2y.

Chapter Topics Types of Regression Models

Identify Linear, Quadratic, and Exponential Functions N Distinguish quadratic and exponential functions as nonlinear using a graph and/or a table.

Calculating Residuals © Christine Crisp “Teach A Level Maths” Vol. 2: A2 Core Modules.

Simple Linear Regression NFL Point Spreads – 2007.

Linear Regression.

Biostatistics Unit 9 – Regression and Correlation.

Section 4.2 Least Squares Regression. Finding Linear Equation that Relates x and y values together Based on Two Points (Algebra) 1.Pick two data points.

Linear Regression Least Squares Method: the Meaning of r 2.

Thomas Knotts. Engineers often: Regress data  Analysis  Fit to theory  Data reduction Use the regression of others  Antoine Equation  DIPPR.

2014. Engineers often: Regress data  Analysis  Fit to theory  Data reduction Use the regression of others  Antoine Equation  DIPPR We need to be.

LBSRE1021 Data Interpretation Lecture 11 Correlation and Regression.

1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.

Regression Lines. Today’s Aim: To learn the method for calculating the most accurate Line of Best Fit for a set of data.

Simple Linear Regression. The term linear regression implies that  Y|x is linearly related to x by the population regression equation  Y|x =  +  x.

© Copyright McGraw-Hill Correlation and Regression CHAPTER 10.

7-5 Graphing linear equations Objectives: Graph linear equations by using the x and y intercepts or the slope and y intercept.

Line of Best Fit 4-8 Warm Up Lesson Presentation Lesson Quiz

9.1B – Computing the Correlation Coefficient by Hand

1 Numbers & Basic Algebra – Math 103 Math, Statistics & Physics.

Unit 3 Sections 9.2 – Day 1.  After we determine that a relationship between two variables exists (correlation), the next step is determine the line.

1 Beginning & Intermediate Algebra – Math 103 Math, Statistics & Physics.

Chapter 3 Test Review Algebra II CP Mrs. Mongold.

Linear Prediction Correlation can be used to make predictions – Values on X can be used to predict values on Y – Stronger relationships between X and Y.

Math 4030 – 11b Method of Least Squares. Model: Dependent (response) Variable Independent (control) Variable Random Error Objectives: Find (estimated)

Engineers often: Regress data to a model  Used for assessing theory  Used for predicting  Empirical or theoretical model Use the regression of others.

y=a+bx Linear Regression: Method of Least Squares slope y intercept y

Class 22. Understanding Regression EMBS Part of 12.7 Sections 1-3 and 7 of Pfeifer Regression note.

MAT 2401 Linear Algebra 2.5 Applications of Matrix Operations

Linear Regression Line of Best Fit. Gradient = Intercept =

Correlation and Regression Chapter 9. § 9.2 Linear Regression.

Regression Modeling Applications in Land use and Transport.

Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:

-last section we wrote an equation of a line using its slope and y-intercept -now, you will write an equation of a line.

4.2 – Linear Regression and the Coefficient of Determination Sometimes we will need an exact equation for the line of best fit. Vocabulary Least-Squares.

Regression lines A line of best fit should: Go through ( x , y )

Linear Regression Essentials Line Basics y = mx + b vs. Definitions

LEAST – SQUARES REGRESSION

CHAPTER 3 Describing Relationships

CHAPTER 10 Correlation and Regression (Objectives)

Chapter 8 – Linear Regression

Linear Regression.

Linear Regression.

Elementary Statistics: Picturing The World

Statistics in WR: Lecture 12

Prediction of new observations

Linear regression Fitting a straight line to observations.

Section 10.2: Fitting a Linear Model to Data

Least Squares Fitting A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the.

Least Squares Method: the Meaning of r2

7.4 – The Method of Least-Squares

Section 2: Linear Regression.

Least-Squares Regression

Lesson 2.2 Linear Regression.

ALGEBRA II HONORS/GIFTED - SECTION 5-3 (Solving Polynomial Equations)

Nonlinear Fitting.

Discrete Least Squares Approximation

CALCULATING EQUATION OF LEAST SQUARES REGRESSION LINE

11C Line of Best Fit By Eye, 11D Linear Regression

y x y = x + 2 y = x + 4 y = x – 1 y = 6x – 3 y = 2x y = ½x y = 3x + 1

Writing Linear Equations in Slope-Intercept Form

Algebra 1 Section 9.5.

Warm up 21 1.) Determine the slope and y intercept of the line y=7x ) Determine the slope and the yintercept of the line 7x- 4y=3 3.) Graph y=1/2.

Indicator 16 System of Equations.

Presentation transcript:

9.2A- Linear Regression Regression Line = Line of best fit The line for which the sum of the squares of the residuals is a minimum Residuals (d) = distance a data point is away from the line

Finding the Line of best fit in Algebra

Find the Equation of the Regression Line with Statistics

Example: X Y XYxyx²y² , , , , , , , ,225 Σx=15.8Σy=1634Σxy=3289.8Σx²=32.44Σy²=337,558

Example; continued

Example Continued m= b= y=mx+b y=50.729x (rounded to 3 places)