LEAST – SQUARES REGRESSION

Slides:



Advertisements
Similar presentations
AP Statistics Section 3.2 C Coefficient of Determination
Advertisements

AP Statistics Section 3.2 B Residuals
Least Squares Regression
AP Statistics.  Least Squares regression is a way of finding a line that summarizes the relationship between two variables.
AP Statistics Chapter 8 Linear Regression.
Statistics Measures of Regression and Prediction Intervals.
Definition  Regression Model  Regression Equation Y i =  0 +  1 X i ^ Given a collection of paired data, the regression equation algebraically describes.
Regression, Residuals, and Coefficient of Determination Section 3.2.
Describing Bivariate Relationships Chapter 3 Summary YMS3e AP Stats at LSHS Mr. Molesky Chapter 3 Summary YMS3e AP Stats at LSHS Mr. Molesky.
AP STATISTICS LESSON 3 – 3 LEAST – SQUARES REGRESSION.
Section 5.2: Linear Regression: Fitting a Line to Bivariate Data.
3.2 Least Squares Regression Line. Regression Line Describes how a response variable changes as an explanatory variable changes Formula sheet: Calculator.
Chapter 14 Inference for Regression AP Statistics 14.1 – Inference about the Model 14.2 – Predictions and Conditions.
Regression Lines. Today’s Aim: To learn the method for calculating the most accurate Line of Best Fit for a set of data.
3.2 - Least- Squares Regression. Where else have we seen “residuals?” Sx = data point - mean (observed - predicted) z-scores = observed - expected * note.
Examining Bivariate Data Unit 3 – Statistics. Some Vocabulary Response aka Dependent Variable –Measures an outcome of a study Explanatory aka Independent.
AP STATISTICS LESSON 14 – 1 ( DAY 1 ) INFERENCE ABOUT THE MODEL.
POD 09/19/ B #5P a)Describe the relationship between speed and pulse as shown in the scatterplot to the right. b)The correlation coefficient, r,
Residuals Recall that the vertical distances from the points to the least-squares regression line are as small as possible.  Because those vertical distances.
3.2 - Residuals and Least Squares Regression Line.
Method 3: Least squares regression. Another method for finding the equation of a straight line which is fitted to data is known as the method of least-squares.
Chapters 8 Linear Regression. Correlation and Regression Correlation = linear relationship between two variables. Summarize relationship with line. Called.
AP STATISTICS LESSON 3 – 3 (DAY 2) The role of r 2 in regression.
Describing Bivariate Relationships. Bivariate Relationships When exploring/describing a bivariate (x,y) relationship: Determine the Explanatory and Response.
CHAPTER 3 Describing Relationships
Unit 4 LSRL.
LSRL.
Lecture #26 Thursday, November 17, 2016 Textbook: 14.1 and 14.3
Least Squares Regression Line.
Statistics 101 Chapter 3 Section 3.
Linear Regression Special Topics.
CHAPTER 3 Describing Relationships
CHAPTER 3 Describing Relationships
Chapter 5 LSRL.
LSRL Least Squares Regression Line
Chapter 3.2 LSRL.
Data Analysis and Statistical Software I ( ) Quarter: Autumn 02/03
Describing Bivariate Relationships
AP Stats: 3.3 Least-Squares Regression Line
LEAST – SQUARES REGRESSION
Regression Models - Introduction
Least-Squares Regression
Least Squares Regression Line LSRL Chapter 7-continued
AP STATISTICS LESSON 3 – 3 (DAY 2)
CHAPTER 3 Describing Relationships
Least-Squares Regression
^ y = a + bx Stats Chapter 5 - Least Squares Regression
CHAPTER 3 Describing Relationships
GET OUT p.161 HW!.
Unit 4 Vocabulary.
Chapter 14 Inference for Regression
Chapter 5 LSRL.
Chapter 5 LSRL.
Least-Squares Regression
Least-Squares Regression
Correlation and Regression
CALCULATING EQUATION OF LEAST SQUARES REGRESSION LINE
CHAPTER 3 Describing Relationships
Chapter 14 Inference for Regression
CHAPTER 3 Describing Relationships
CHAPTER 3 Describing Relationships
Lesson – How can I measure my linear fit? - Correlations
CHAPTER 3 Describing Relationships
Tuesday, September 29 Check HW Probs 3.13, 14, 20 (7-11-doubles)
CHAPTER 3 Describing Relationships
A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. Find the correlation coefficient & interpret.
Least Squares Regression Chapter 3.2
Chapter 14 Multiple Regression
Regression Models - Introduction
CHAPTER 3 Describing Relationships
Presentation transcript:

LEAST – SQUARES REGRESSION AP STATISTICS LESSON 3 – 3 LEAST – SQUARES REGRESSION

Regression Line A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x. Regression, unlike correlation, requires we have an explanatory variable and a response variable. LSRL – Is the abbreviation for least squares regression line. LSRL is a mathematical model.

Least – squares Regression Line Error = observed – predicted To find the most effective model we must square the errors and sum them to find the least errors squared.

Least – squares Regression Line The least – squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

Equation of the least –squares regression line We have data on an explanatory variable x and a response variable y for n individuals. Form the data, calculate the means x and y and the standard deviations s

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com. Inc. All rights reserved.