Warm-up with 3.3 Notes on Correlation Universities use SAT scores in the admissions process because they believe these scores provide some insight into.

Slides:

Advertisements

Similar presentations

Chapter 3 Examining Relationships Lindsey Van Cleave AP Statistics September 24, 2006.

Advertisements

Scatterplots and Correlation

Least Squares Regression

LSRLs: Interpreting r vs. r2

Lesson Diagnostics on the Least- Squares Regression Line.

Chapter 3 Bivariate Data

2nd Day: Bear Example Length (in) Weight (lb)

AP Statistics Mrs Johnson

Haroon Alam, Mitchell Sanders, Chuck McAllister- Ashley, and Arjun Patel.

C HAPTER 3: E XAMINING R ELATIONSHIPS. S ECTION 3.3: L EAST -S QUARES R EGRESSION Correlation measures the strength and direction of the linear relationship.

Warm-up with Multiple Choice Practice on 3.1 to 3.3

Warm-up A. P Stats Shape-Changing Transformations/ Stats – 3.4 Diagonstics Copy the two columns and match them.

Warm-up with 3.3 Notes on Correlation The fat and calorie contents of 5oz of 3 kinds of pizza are represented by the data points (9, 305), (11, 309)

Warm-up Ch. 3 Practice Test

Warm-up 3.2 Getting a line on the pattern Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would.

Warm-up with 3.3 Notes on Correlation

Lesson Least-Squares Regression. Knowledge Objectives Explain what is meant by a regression line. Explain what is meant by extrapolation. Explain.

Least-Squares Regression Section 3.3. Why Create a Model? There are two reasons to create a mathematical model for a set of bivariate data. To predict.

Warm-up 3.4 Diagnostic of Influential Points 4) 5) 6)

AP STATISTICS LESSON 3 – 3 LEAST – SQUARES REGRESSION.

Chapter 3 Section 3.1 Examining Relationships. Continue to ask the preliminary questions familiar from Chapter 1 and 2 What individuals do the data describe?

Section 2.2 Correlation A numerical measure to supplement the graph. Will give us an indication of “how closely” the data points fit a particular line.

Lesson Scatterplots and Correlation. Knowledge Objectives Explain the difference between an explanatory variable and a response variable Explain.

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

AP Statistics Chapter 27 Notes “Inference for Regression”

TODAY we will Review what we have learned so far about Regression Develop the ability to use Residual Analysis to assess if a model (LSRL) is appropriate.

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

Correlation The apparent relation between two variables.

S CATTERPLOTS Correlation, Least-Squares Regression, Residuals Get That Program ANSCOMBE CRICKETS GESSEL.

Chapter 3-Examining Relationships Scatterplots and Correlation Least-squares Regression.

Chapter 14: Inference for Regression. A brief review of chapter 4... (Regression Analysis: Exploring Association BetweenVariables )  Bi-variate data.

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,

3.2 Least-Squares Regression Objectives SWBAT: INTERPRET the slope and y intercept of a least-squares regression line. USE the least-squares regression.

 Chapter 3! 1. UNIT 7 VOCABULARY – CHAPTERS 3 & 14 2.

2.5 Using Linear Models P Scatter Plot: graph that relates 2 sets of data by plotting the ordered pairs. Correlation: strength of the relationship.

Linear Regression Day 1 – (pg )

^ 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.

LSRLs: Interpreting r vs. r 2 r – “the correlation coefficient” tells you the strength and direction between two variables (x and y, for example, height.

Section 1.3 Scatter Plots and Correlation.  Graph a scatter plot and identify the data correlation.  Use a graphing calculator to find the correlation.

Unit 3 – Association: Contingency, Correlation, and Regression Lesson 3-2 Quantitative Associations.

Describing Relationships. Least-Squares Regression  A method for finding a line that summarizes the relationship between two variables Only in a specific.

1. Analyzing patterns in scatterplots 2. Correlation and linearity 3. Least-squares regression line 4. Residual plots, outliers, and influential points.

Warm-up Get a sheet of computer paper/construction paper from the front of the room, and create your very own paper airplane. Try to create planes with.

Bring project data to enter into Fathom

The Least Square Regression Line (LSRL) is:

Chapter 4.2 Notes LSRL.

Least Squares Regression Line.

Sections Review.

Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions.

LSRL Least Squares Regression Line

Chapter 3.2 LSRL.

Exercise 4 Find the value of k such that the line passing through the points (−4, 2k) and (k, −5) has slope −1.

2.5 Scatterplots and Lines of Regression

AP Stats: 3.3 Least-Squares Regression Line

Least-Squares Regression

Least Squares Regression Line LSRL Chapter 7-continued

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

Do Now Create a scatterplot following these directions

Do Now Describe the following relationships. Do Now Describe the following relationships.

Chapter 5 LSRL.

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: Describing Relationships

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;

Presentation transcript:

Warm-up with 3.3 Notes on Correlation Universities use SAT scores in the admissions process because they believe these scores provide some insight into how a high school student will perform at the college level. Suppose the entering freshmen at a certain college have mean combined SAT scores of 1222 with a standard deviation of 83. In the first semester these students attained a mean GPA of 2.66 with a standard deviation of A scatterplot showed the association to be reasonably linear, and the correlation between SAT score and GPA was a) Identify the following: b) If r is the correlation calculate the slope b 1. c) Plug in and b 1 to solve for b 0 (y-intercept). d) Write the equation of the regression line.

Student of the day! Block 1

Student of the day! Block 2

H.W. Discussion 3.2 P#3 and 4; E#9 and 10

Calculating the LSRL step-by-step A high school counselor wants to see if there is a correlation between GPA and SAT score. Here are some of the data the guidance counselor is looking at. Sum: _____ _____ _____ ______ _______ _______ Mean: ____ _____ _____ _____ to find the b o substitute ( )

Use the calculator to find the LSRL STAT = > CALC Select #8 LinReg(a + bx) To get correlation go to 2 nd 0 for Catalog hit x -1 for D. Find DiagonsticOn highlight it and hit ENTER two times.

3.3 Correlation Correlation tells you the strength of the trend. OR r 2 is the coefficient of determination. It is the proportion of variation of the response variable that can be explained by the explanatory variable.

How to see the residual plot on the calculator! If the regression line is a good model, we would expect to find the residuals more or less randomly scattered about the average residual which is represented by the horizontal line. No pattern on the residual plot means the data could be represented by a linear model.

Finding Correlation Coefficient on the Calculator In order to find r (correlation coefficient) on your calculator. We need to change it from the factory setting by going to CATALOG (Hit 2 nd the 0  zero). When in CATALOG your keys are automatically in Alpha so hit x -1 (where the Green D is located) Scroll down to DiagnosticOn and press Enter twice! Practice: Speed: MPG: STAT -> Calc Scroll down to 8: LinReg(a+bx) Enter LineReg(a +bx) L 1, L 2, Y 1 Enter Notice you get both r and r 2 ! Any theories about the r in this problem? Look at the graph.

Let’s look at the residual plot

Investigation of Scatter plots and Residuals Any observations on the two Data Sets? Remember to use Zoom #9 Zoom Stat Each time. Homework 3.3 Pg 141 P#15 and 16, E#27 and 28

Ch. 1 Test Double-checked, 12# on FORM A, if you answered C, you got it right. My answer key was wrong. Bring me your test if your original answer was A on #12 if you had FORM A.

Monday is 3.1 to 3.3 Quiz Know all vocabulary and formulas from 3.1 to 3.3 Know how create a scatter plot and find the Line of best fit. Know how to calculate the LSRL, how to extrapolate and calculate the residual for a particular piece of data. Be able to interpret the slope and y-intercept in the context of the problem Know how to describe scatter plots: Shape, Trend Strength and under Shape: Linearity, Clusters and outlier. Know how to calculate the SSE

Answers to A.P. Statistics H.W. 3.2 P#3 and 4, E # 9 and 11 P4. a. The slope is about 0.8 b. This means as hand length increases by 1 cm, the width would increase by 0.8 cm. c. d. A possible explanation is that the points represent those students that measured hand width by not spreading fingers apart. If the cluster of points below was removed then the slope becomes steeper. P5.

E #9 E #10