Linear Regression. Scatterplot: Regression Line: Correlation: A line that describes how a response variable y changes as an explanatory variable x changes.

Slides:

Advertisements

Similar presentations

AP Statistics Section 3.1B Correlation

Advertisements

Scatterplots and Correlation

Chapter 3 Examining Relationships

AP Statistics.  Least Squares regression is a way of finding a line that summarizes the relationship between two variables.

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

7.1 Seeking Correlation LEARNING GOAL

Scatter Diagrams and Linear Correlation

Linear Regression (C7-9 BVD). * Explanatory variable goes on x-axis * Response variable goes on y-axis * Don’t forget labels and scale * Statplot 1 st.

MAT 105 SPRING 2009 Quadratic Equations

Warm up Use calculator to find r,, a, b. Chapter 8 LSRL-Least Squares Regression Line.

Correlation Correlation is the relationship between two quantitative variables. Correlation coefficient (r) measures the strength of the linear relationship.

CHAPTER 4: Scatterplots and Correlation

LSRL Least Squares Regression Line

All about Regression Sections Section 10-4 regression Objectives ◦Compute the equation of the regression line ◦Make a prediction using the.

Calculating and Interpreting the Correlation Coefficient ~adapted from walch education.

5-7 Scatter Plots. _______________ plots are graphs that relate two different sets of data by displaying them as ordered pairs. Usually scatter plots.

VCE Further Maths Least Square Regression using the calculator.

Descriptive Statistics: Correlation u Describes the relationship between two or more variables. u Describes the strength of the relationship in terms of.

CHAPTER 4: Scatterplots and Correlation ESSENTIAL STATISTICS Second Edition David S. Moore, William I. Notz, and Michael A. Fligner Lecture Presentation.

Correlation Correlation measures the strength of the LINEAR relationship between 2 quantitative variables. Labeled as r Takes on the values -1 < r < 1.

Objective: I can write linear equations that model real world data.

Chapter 6: Exploring Data: Relationships Lesson Plan Displaying Relationships: Scatterplots Making Predictions: Regression Lines Correlation Least-Squares.

Warm Up 1.What is a scatterplot? 2.How do I create one? 3.What does it tell me? 4.What 3 things do we discuss when analyzing a scatterplot?

4.2 Introduction to Correlation Objective: By the end of this section, I will be able to… Calculate and interpret the value of the correlation coefficient.

2-5: Using Linear Models Algebra 2 CP. Scatterplots & Correlation Scatterplot ◦ Relates two sets of data ◦ Plots the data as ordered pairs ◦ Used to tell.

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?

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

Example 1: page 161 #5 Example 2: page 160 #1 Explanatory Variable - Response Variable - independent variable dependent variable.

Section 4.1 Scatter Diagrams and Correlation. Definitions The Response Variable is the variable whose value can be explained by the value of the explanatory.

Bivariate Data and Scatter Plots Bivariate Data: The values of two different variables that are obtained from the same population element. While the variables.

Relationships If we are doing a study which involves more than one variable, how can we tell if there is a relationship between two (or more) of the.

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

Chapter 4 - Scatterplots and Correlation Dealing with several variables within a group vs. the same variable for different groups. Response Variable:

 Describe the association between two quantitative variables using a scatterplot’s direction, form, and strength  If the scatterplot’s form is linear,

Do Now Women (x): Men (y): Using your calculator, make a scatterplot. Describe the direction, strength, form, and any outliers.

Warm-Up Write the equation of each line. A B (1,2) and (-3, 7)

Scatter Plots, Correlation and Linear Regression.

2.5 Using Linear Models A scatter plot is a graph that relates two sets of data by plotting the data as ordered pairs. You can use a scatter plot to determine.

Objective: To write linear equations that model real-world data. To make predictions from linear models. Bell Ringer: Write 3 ways you used math over your.

9.1 - Correlation Correlation = relationship between 2 variables (x,y): x= independent or explanatory variable y= dependent or response variable Types.

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,

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.

SWBAT: Calculate and interpret the equation of the least-squares regression line Do Now: If data set A of (x, y) data has correlation r = 0.65, and a second.

Yes no = -9= 0 = -4 = -5/6.  Students will learn: ◦ To write an equation for a line of best fit and use it to make predictions. The trend line that.

Scatterplots and Linear Regressions Unit 8. Warm – up!! As you walk in, please pick up your calculator and begin working on your warm – up! 1. Look at.

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

C HAPTER 3: E XAMINING R ELATIONSHIPS. 3.2: C ORRELATION Measures the direction and strength of a linear relationship between two variables. Usually written.

Scatter Plot A scatter plot is a graph of a collection of ordered pairs (x,y). The ordered pairs are not connected The graph looks like a bunch of dots,

The coefficient of determination, r 2, is The fraction of the variation in the value of y that is explained by the regression line and the explanatory.

Entry Task Write the equation in slope intercept form and find the x and y intercepts. 1. 4x + 6y = 12.

1.5 Linear Models Warm-up Page 41 #53 How are linear models created to represent real-world situations?

Scatter Plots and Correlations. Is there a relationship between the amount of gas put in a car and the number of miles that can be driven?

Response Variable: measures the outcome of a study (aka Dependent Variable) Explanatory Variable: helps explain or influences the change in the response.

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

Two-Variable Data Analysis

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.

Describing Bivariate Relationships

Do Now Create a scatterplot following these directions

Examining Relationships

Describing Bivariate Relationships

Linear Models We will determine and use linear models, and use correlation coefficients.

LEARNING GOALS FOR LESSON 2.7

Correlation & Trend Lines

Section 11.1 Correlation.

Modeling a Linear Relationship

Presentation transcript:

Linear Regression

Scatterplot: Regression Line: Correlation: A line that describes how a response variable y changes as an explanatory variable x changes. Used to predict the values of y for a given value of x. r-value Measures the strength and direction of the linear relationship between two quantitative variables Always between -1 and 1. Shows the relationship between two quantitative variables measured on the same graph. Each point is an (x,y) coordinate Form: y = a + bx *be sure to label x- & y –axis and 2 points!

Interpretations Slope: Correlation: direction, strength, linearxy There is a direction, strength, linear of association between x and y Direction: Direction: positive or negative Strength: Strength: Strong, Moderate, or Weak Linear: Linear: *if scatterplot appears to be linear, it is linear Form: y = a + bx a = y-intercept b = slope unitx increase/decreaseby For each unit increase in x, there is an approximate increase/decrease of b in y.

Example 1: The following data are advertised horsepower and expected gas mileage for several 2007 vehicles a) Create a scatterplot of these data b) Find the regression line and correlation. c) Interpret the slope and correlation. VehicleHorsepowerHighway Gas Mileage (MPG) Audi A BMW Buick LaCrosse20030 Chevy Cobalt14832 Chevy Trailblazer29122 Ford Expedition30020 GMC Yukon29521 Honda Civic14040 Honda Accord16634 Hyundai Elantra13838 Lexus IS Lincoln Navigator30018 Mazda Tribute21225 Toyota Camry15834 VW Beetle15030

Calculator Screens—Create Scatterplot 1)Enter data into L1 and L2 2)Create Scatterplot using L1 and L2 3)Zoom – 9: ZoomStat

Calculator Screens–Regression Line 1)STAT -- CALC 2)8: LinReg (a+ bx) XList: L1 Ylist: L2 3) Calculate

Example 1: a) Create a scatterplot of these data b) Find the regression line and correlation. y = x r = -.87 Slope: For each unit increase in horsepower, there is an approximate decrease of.086 miles per gallon in Highway Gas Mileage. Correlation: There is a strong, negative linear relationship between horsepower and gas mileage.

Example 2: The data for 11 stand mixers is given below. a)Create a scatterplot of the data. b)Find the regression line and correlation. c)Interpret slope and correlation. d)Find the price for a mixer that weighs 20 pounds. y= x r =.74 Slope: For each 1-pound increase in weight, there is an approximate increase of $12.53 in price. Correlation: There is a positive, moderate linear relationship between weight and price. y = (20) = $229.89Approximately $ Weight (pounds)Price (dollars)