Stats for Engineers Lecture 9. Summary From Last Time Confidence Intervals for the mean t-tables Q Student t-distribution.

Slides:

Advertisements

Similar presentations

Modeling of Data. Basic Bayes theorem Bayes theorem relates the conditional probabilities of two events A, and B: A might be a hypothesis and B might.

Advertisements

Lecture 17: Tues., March 16 Inference for simple linear regression (Ch ) R2 statistic (Ch ) Association is not causation (Ch ) Next.

11-1 Empirical Models Many problems in engineering and science involve exploring the relationships between two or more variables. Regression analysis.

6-1 Introduction To Empirical Models 6-1 Introduction To Empirical Models.

Linear regression models

Simple Linear Regression

© 2010 Pearson Prentice Hall. All rights reserved Least Squares Regression Models.

Chapter 10 Simple Regression.

REGRESSION Want to predict one variable (say Y) using the other variable (say X) GOAL: Set up an equation connecting X and Y. Linear regression linear.

Stat 200b. Chapter 8. Linear regression models.. n by 1, n by 2, 2 by 1, n by 1.

Descriptive statistics Experiment  Data  Sample Statistics Experiment  Data  Sample Statistics Sample mean Sample mean Sample variance Sample variance.

Probability & Statistics for Engineers & Scientists, by Walpole, Myers, Myers & Ye ~ Chapter 11 Notes Class notes for ISE 201 San Jose State University.

Lecture 16 – Thurs, Oct. 30 Inference for Regression (Sections ): –Hypothesis Tests and Confidence Intervals for Intercept and Slope –Confidence.

Simple Linear Regression Analysis

Statistics 350 Lecture 17. Today Last Day: Introduction to Multiple Linear Regression Model Today: More Chapter 6.

Lecture 19 Simple linear regression (Review, 18.5, 18.8)

Simple Linear Regression and Correlation

Simple Linear Regression Analysis

1 1 Slide Simple Linear Regression Chapter 14 BA 303 – Spring 2011.

Correlation & Regression

Chapter 11 Simple Regression

Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Chapter Inference on the Least-Squares Regression Model and Multiple Regression 14.

1 Dr. Jerrell T. Stracener EMIS 7370 STAT 5340 Probability and Statistics for Scientists and Engineers Department of Engineering Management, Information.

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

Statistical Methods Statistical Methods Descriptive Inferential

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 4 Section 2 – Slide 1 of 20 Chapter 4 Section 2 Least-Squares Regression.

Inference for Regression Simple Linear Regression IPS Chapter 10.1 © 2009 W.H. Freeman and Company.

Multiple Regression Petter Mostad Review: Simple linear regression We define a model where are independent (normally distributed) with equal.

1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k.

Simple Linear Regression. The term linear regression implies that  Y|x is linearly related to x by the population regression equation  Y|x =  +  x.

STA 286 week 131 Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression.

Multiple Regression. Simple Regression in detail Y i = β o + β 1 x i + ε i Where Y => Dependent variable X => Independent variable β o => Model parameter.

AP STATISTICS LESSON 14 – 1 ( DAY 1 ) INFERENCE ABOUT THE MODEL.

Least Squares Regression.   If we have two variables X and Y, we often would like to model the relation as a line  Draw a line through the scatter.

Chapter 10: Determining How Costs Behave 1 Horngren 13e.

I271B QUANTITATIVE METHODS Regression and Diagnostics.

June 30, 2008Stat Lecture 16 - Regression1 Inference for relationships between variables Statistics Lecture 16.

Curve Fitting Pertemuan 10 Matakuliah: S0262-Analisis Numerik Tahun: 2010.

© 2001 Prentice-Hall, Inc.Chap 13-1 BA 201 Lecture 18 Introduction to Simple Linear Regression (Data)Data.

Lesson 14 - R Chapter 14 Review. Objectives Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review.

Stats of Engineers, Lecture 8. 1.If the sample mean was larger 2.If you increased your confidence level 3.If you increased your sample size 4.If the population.

Chapter 11: Linear Regression and Correlation Regression analysis is a statistical tool that utilizes the relation between two or more quantitative variables.

1 Simple Linear Regression and Correlation Least Squares Method The Model Estimating the Coefficients EXAMPLE 1: USED CAR SALES.

1 1 Slide The Simple Linear Regression Model n Simple Linear Regression Model y =  0 +  1 x +  n Simple Linear Regression Equation E( y ) =  0 + 

Intro to Statistics for the Behavioral Sciences PSYC 1900 Lecture 7: Regression.

ESTIMATION METHODS We know how to calculate confidence intervals for estimates of  and  2 Now, we need procedures to calculate  and  2, themselves.

1 AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Part II: Theory and Estimation of Regression Models Chapter 5: Simple Regression Theory.

Simple linear regression. What is simple linear regression? A way of evaluating the relationship between two continuous variables. One variable is regarded.

Statistics 350 Lecture 2. Today Last Day: Section Today: Section 1.6 Homework #1: Chapter 1 Problems (page 33-38): 2, 5, 6, 7, 22, 26, 33, 34,

Statistics 350 Review. Today Today: Review Simple Linear Regression Simple linear regression model: Y i =  for i=1,2,…,n Distribution of errors.

Linear Regression Hypothesis testing and Estimation.

The “Big Picture” (from Heath 1995). Simple Linear Regression.

Simple linear regression. What is simple linear regression? A way of evaluating the relationship between two continuous variables. One variable is regarded.

Bivariate Regression. Bivariate Regression analyzes the relationship between two variables. Bivariate Regression analyzes the relationship between two.

STA302/1001 week 11 Regression Models - Introduction In regression models, two types of variables that are studied:  A dependent variable, Y, also called.

The simple linear regression model and parameter estimation

Regression and Correlation of Data Summary

Statistics 350 Lecture 3.

Ch12.1 Simple Linear Regression

Simple Linear Regression - Introduction

Statistical Methods For Engineers

Linear Regression.

Regression Models - Introduction

Linear regression Fitting a straight line to observations.

BA 275 Quantitative Business Methods

Simple Linear Regression

Simple Linear Regression

Regression Statistics

Simple Linear Regression

Regression Models - Introduction

Presentation transcript:

Stats for Engineers Lecture 9

Summary From Last Time Confidence Intervals for the mean t-tables Q Student t-distribution

Sample size How many random samples do you need to reach desired level of precision? Want Need:

Answer: Assuming plates have independent weights with a Normal distribution i.e. need to test about 28

Linear regression

e.g.

e.g.

Or is it What do we mean by a line being a ‘good fit’?

Simple model for data: Random errorStraight line - Linear regression model

Maximum likelihood estimate = least -squares estimate Minimize Data pointStraight-line prediction E is defined and can be minimized even when errors not Normal – least-squares is simple general prescription for fitting a straight line (but statistical interpretation in general less clear) Want to estimate parameters a and b, using the data.

Question from Derek Bruff

Where Sample means Equation of the fitted line is

Most of the things you need to use are on the formula sheet

y x Example: The data y has been observed for various values of x, as follows: Fit the simple linear regression model using least squares. Answer:

Which of the following data are likely to be most appropriately modelled using a linear regression model?

[derivation in notes] Quantifying the goodness of the fit Residual sum of squares

Question from Derek Bruff