A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. DosageHeart rate 0.12595 0.290 0.2593.

Slides:

Advertisements

Similar presentations

AP Statistics Section 3.2 C Coefficient of Determination

Advertisements

Chapter 3 Bivariate Data

LSRL Least Squares Regression Line

Regression, Residuals, and Coefficient of Determination Section 3.2.

Linear Regression Analysis

Section 4.2 Regression Equations and Predictions.

AP STATISTICS LESSON 3 – 3 LEAST – SQUARES REGRESSION.

Section 5.2: Linear Regression: Fitting a Line to Bivariate Data.

Chapter 10 Correlation and Regression

3.2 Least Squares Regression Line. Regression Line Describes how a response variable changes as an explanatory variable changes Formula sheet: Calculator.

Regression Regression relationship = trend + scatter

3.2 - Least- Squares Regression. Where else have we seen “residuals?” Sx = data point - mean (observed - predicted) z-scores = observed - expected * note.

WARM-UP Do the work on the slip of paper (handout)

Examining Bivariate Data Unit 3 – Statistics. Some Vocabulary Response aka Dependent Variable –Measures an outcome of a study Explanatory aka Independent.

CHAPTER 5 Regression BPS - 5TH ED.CHAPTER 5 1. PREDICTION VIA REGRESSION LINE NUMBER OF NEW BIRDS AND PERCENT RETURNING BPS - 5TH ED.CHAPTER 5 2.

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

AP STATISTICS Section 3.2 Least Squares Regression.

SWBAT: Calculate and interpret the residual plot for a line of regression Do Now: Do heavier cars really use more gasoline? In the following data set,

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,

A P STATISTICS LESSON 3 – 3 (DAY 3) A P STATISTICS LESSON 3 – 3 (DAY 3) RISIDUALS.

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. Chapter 3 Association: Contingency, Correlation, and Regression Section 3.3 Predicting the Outcome.

^ y = a + bx Stats Chapter 5 - Least Squares Regression

LEAST-SQUARES REGRESSION 3.2 Least Squares Regression Line and Residuals.

Warm-up O Turn in HW – Ch 8 Worksheet O Complete the warm-up that you picked up by the door. (you have 10 minutes)

LEAST-SQUARES REGRESSION 3.2 Role of s and r 2 in Regression.

Least Squares Regression Lines Text: Chapter 3.3 Unit 4: Notes page 58.

Unit 4 Lesson 3 (5.3) Summarizing Bivariate Data 5.3: LSRL.

Simple Linear Regression The Coefficients of Correlation and Determination Two Quantitative Variables x variable – independent variable or explanatory.

Chapter 7 Linear Regression. Bivariate data x – variable: is the independent or explanatory variable y- variable: is the dependent or response variable.

Chapter 5 Lesson 5.2 Summarizing Bivariate Data 5.2: LSRL.

Chapters 8 Linear Regression. Correlation and Regression Correlation = linear relationship between two variables. Summarize relationship with line. Called.

Part II Exploring Relationships Between Variables.

Describing Bivariate Relationships. Bivariate Relationships When exploring/describing a bivariate (x,y) relationship: Determine the Explanatory and Response.

Chapter 3 LSRL. Bivariate data x – variable: is the independent or explanatory variable y- variable: is the dependent or response variable Use x to predict.

Chapter 5 LSRL. Bivariate data x – variable: is the independent or explanatory variable y- variable: is the dependent or response variable Use x to predict.

Least Square Regression Line. Line of Best Fit Our objective is to fit a line in the scatterplot that fits the data the best As just seen, the best fit.

CHAPTER 3 Describing Relationships

CHAPTER 3 Describing Relationships

Least Squares Regression Line.

Statistics 101 Chapter 3 Section 3.

CHAPTER 3 Describing Relationships

Chapter 5 LSRL.

LSRL Least Squares Regression Line

Chapter 3.2 LSRL.

Warm Up Go ahead and start wrapping up your Guess My Age projects.

The Least-Squares Regression Line

Data Analysis and Statistical Software I ( ) Quarter: Autumn 02/03

Linear Regression.

Least-Squares Regression

Least Squares Regression Line LSRL Chapter 7-continued

EQ: How well does the line fit the data?

Least-Squares Regression

^ y = a + bx Stats Chapter 5 - Least Squares Regression

CHAPTER 3 Describing Relationships

GET OUT p.161 HW!.

Chapter 5 LSRL.

Chapter 5 LSRL.

Chapter 5 LSRL.

Least-Squares Regression

Least-Squares Regression

Ch 4.1 & 4.2 Two dimensions concept

Section 3.2: Least Squares Regressions

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.

Chapter 3 Vocabulary Linear Regression.

Residuals (resids).

Homework: PG. 204 #30, 31 pg. 212 #35,36 30.) a. Reading scores are predicted to increase by for each one-point increase in IQ. For x=90: 45.98;

Review of Chapter 3 Examining Relationships

Presentation transcript:

A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. DosageHeart rate Find the correlation coefficient & interpret it. 2.Find & interpret the slope. 3.Find & interpret the y-intercept. 4.Give the least squares regression line.

A medical researcher wishes to determine how the dosage (in mg) of a drug affects the heart rate of the patient. DosageHeart rate

RESIDUALS Section 3.2B

Residuals

DosageHeart rate Find the predicted value for a dosage of 0.4 mg. 2.Find the residual for (0.4, 80).

DosageHeart rate * The sum of the residuals is always zero!

Residual Plot It is a scatterplot of the residuals vs the explanatory variable. They help us to assess how well a regression line fits the data. The residual plot should show no obvious pattern The residuals should be relatively small.

DosageHeart rate * The sum of the residuals is always zero!

Residual Plot

Height vs Shoe size – residual plot Good residual plot – show relatively no pattern.

Good or Bad

Standard Deviation of the Residuals

DosageHeart rate

Homework *Page 191 (43, 45, 55, 60, 62)