Residuals.

Slides:

Advertisements

Similar presentations

5.4 Correlation and Best-Fitting Lines

Advertisements

7.7 Choosing the Best Model for Two-Variable Data p. 279.

From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A.

1. What is the probability that a randomly selected person is a woman who likes P.E.? 2. Given that you select a man, what is the probability that he likes.

1 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. Summarizing Bivariate Data Introduction to Linear Regression.

Fitting a Function to Data Adapted from Walch Education.

Residuals and Residual Plots Most likely a linear regression will not fit the data perfectly. The residual (e) for each data point is the ________________________.

Correlation with a Non - Linear Emphasis Day 2.  Correlation measures the strength of the linear association between 2 quantitative variables.  Before.

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.

Correlation & Regression – Non Linear Emphasis Section 3.3.

 The equation used to calculate Cab Fare is y = 0.75x where y is the cost and x is the number of miles traveled. 1. What is the slope in this equation?

Analysis of Residuals Data = Fit + Residual. Residual means left over Vertical distance of Y i from the regression hyper-plane An error of “prediction”

Regression Regression relationship = trend + scatter

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

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.

Scatter Plots And Looking at scatter plots Or Bivariate Data.

Get out the Notes from Monday Feb. 4 th, Example 2: Consider the table below displaying the percentage of recorded music sales coming from music.

Creating a Residual Plot and Investigating the Correlation Coefficient.

Section 2.6 – Draw Scatter Plots and Best Fitting Lines A scatterplot is a graph of a set of data pairs (x, y). If y tends to increase as x increases,

Line of Best Fit 4.2 A. Goal Understand a scatter plot, and what makes a line a good fit to data.

7-3 Line of Best Fit Objectives

Holt Algebra Modeling Real-World Data Warm Up quadratic: y ≈ 2.13x 2 – 2x x35813 y Use a calculator to perform quadratic and.

Copyright © 2003, N. Ahbel Residuals. Copyright © 2003, N. Ahbel Predicted Actual Actual – Predicted = Error Source:

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)

Residual Plots Unit #8 - Statistics.

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

Identifying from an equation: Linear y = mx +b Has an x with no exponent (or exponent 1). Examples: y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic y = ax 2 +

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

Residuals. Why Do You Need to Look at the Residual Plot? Because a linear regression model is not always appropriate for the data Can I just look at the.

Residuals, Influential Points, and Outliers

REGRESSION MODELS OF BEST FIT Assess the fit of a function model for bivariate (2 variables) data by plotting and analyzing residuals.

Introductory Statistics. Inference for Bivariate Data Intro to Inference in Regression Requirements for Linear Regression Linear Relationship Constant.

Linear Regression Special Topics.

CHAPTER 3 Describing Relationships

distance prediction observed y value predicted value zero

Model validation and prediction

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

Residuals From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A.

Introduction The fit of a linear function to a set of data can be assessed by analyzing residuals. A residual is the vertical distance between an observed.

Homework: Residuals Worksheet

Warm-Up . Math Social Studies P.E. Women Men 2 10

2.5 Correlation and Best-Fitting Lines

Residuals From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A.

Residuals Learning Target:

Describing Bivariate Relationships

Linear Models and Equations

Examining Relationships

Warm-Up 8/50 = /20 = /50 = .36 Math Social Studies P.E.

Chapter 3 Describing Relationships Section 3.2

Residuals and Residual Plots

~adapted for Walch Education

Review Homework.

Review Homework.

Comparing Linear, Exponential, and Quadratic Functions.

Residuals, Influential Points, and Outliers

Review Homework.

Review Homework.

Comparing Linear, Exponential, and Quadratic Functions.

Residuals From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A.

Ch 4.1 & 4.2 Two dimensions concept

Introduction The fit of a linear function to a set of data can be assessed by analyzing residuals. A residual is the vertical distance between an observed.

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.

Draw Scatter Plots and Best-Fitting Lines

Monday, March 10th Warm Up To find the residual you take the ACTUAL data and ______________ the PREDICTED data. If the residual plot creates a pattern.

Warm-Up . Math Social Studies P.E. Women Men 2 10

Residuals From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A.

Residuals and Residual Plots

Presentation transcript:

Residuals

Observed Y – Predicted Y Residuals (Error) The difference between the observed y and the predicted y Observed Y – Predicted Y Determines the effectiveness of the regression model Given to you in the chart Get by plugging into the equation

Residual Plots Determine If the model is appropriate, then the plot will have a random scatter. If another model is necessary, the plot will have a noticeable pattern. Pattern = Problem!

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does there appear to be a pattern in the residual plot? Yes, this shape is called a quadratic. 2. Does this support your original guess? You must now see that a linear model does NOT fit this data. Not scattered!

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does their appear to be a pattern in the residual plot? Yes, it fans out as x increases. 2. Does this support your original guess? You must now see that a linear model does NOT fit this data. Fan Pattern.

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does their appear to be a pattern in the residual plot? Yes, it looks quadratic. 2. Does this support your original guess? This was very tricky. The scale was very small. You must now see that a linear model does NOT fit this data.

Linear model appropriate or inappropriate?

The only way to know is to see the residual plot. 1. Does their appear to be a pattern in the residual plot? Yes, it seems to decrease as x increases. 2. Does this support your original guess? This was tricky. You must now see that a linear model does NOT fit this data.

Example 1: Calculate Residual from this data set: Y Predicted Residuals (observed – predicted) 1 4 2 12 3 18 23 5 24 6 28 = 6.67 -2.67 = Data from TI Activity for NUMB3RS Episode 202 = = =

Example 1: Calculate Residual from this data set: Y Predicted Residuals (observed – predicted) 1 4 6.67 -2.67 2 12 11.27 3 18 15.87 23 20.47 5 24 25.07 6 28 29.67 = = Data from TI Activity for NUMB3RS Episode 202 = = =

Good fit or not? Is there a Pattern? There is no pattern. This makes this line a good fit.

Example 2: Calculate Residual Tracking Cell Phone Use over 10 days Total Time (minutes) Total Distance (miles Predicted Total Distance Residuals (observed – predicted) 32 51 54.4 -3.4 19 30 31.9 28 47 36 56 17 27 23 35 41 65 22 37 73 54 = = = = = Data from TI Activity for NUMB3RS Episode 202 = = = = =

Example: Calculate Residual Tracking Cell Phone Use over 10 days Total Time (minutes) Total Distance (miles) Predicted Total Distance Residuals (observed – predicted) 32 51 54.4 -3.4 19 30 31.9 -1.9 28 47 47.5 -0.5 36 56 61.3 -5.3 17 27 28.5 -1.5 23 35 38.8 -3.8 41 65 70.0 -5 22 37.1 3.9 37 73 63.1 9.9 54 6.5 Data from TI Activity for NUMB3RS Episode 202

Good fit or not? Is there a Pattern? The plots begin to fan out in a “U” shape, so it is not a great fitting line. YES, I THINK THIS STUFF IS HARD TOO!

Homework : Residuals worksheet We will go over this tomorrow in detail, I promise 