Wed, June 26, (Lecture 8-2). Nonlinearity. Significance test for correlation R-squared, SSE, and SST. Correlation in SPSS.
|
|
- Stewart Joseph
- 5 years ago
- Views:
Transcription
1 Wed, June 26, (Lecture 8-2). Nonlinearity. Significance test for correlation R-squared, SSE, and SST. Correlation in SPSS.
2 Last time, we looked at scatterplots, which show the interaction between two variables, and correlation.
3 The correlation coefficient r measures how well the pairs of values fit on a line. r is positive when two values increase together. r is negative when two one value goes up as the other goes down.
4 However, correlation only shows the linear relation between two variables. The variables could still be related in a non-linear way and have little or no correlation.
5 In real world contexts, the most common form of non-linear relationship is a curvilinear one. (SOURCE: GAPMINDER.ORG) One common reason is a scaling issue, where a fixed change in one thing doesn t mean a fixed change in another.
6 Life expectancy increases with the logarithm of income, not with income. (SOURCE: GAPMINDER.ORG) When we rescale income into a log-scale (a scale that shows very small and very large numbers equally well), a line appears.
7 Another reason for non-linearity could be two competing factors. In a too-easy course, nobody learns anything new. In a too-hard course, nobody learns anything at all.
8 Spearman correlation is a measure that can handle curves as long as the trend doesn t switch between increasing and decreasing. The only time we ll be using this is as a check in SPSS. Everything else we do in Ch.10 and 11 is the Pearson correlation, which is restricted to linear relationships. We use the Pearson correlation because it produces stronger results and the math is simpler.
9 Math: The ugly sweater around an otherwise pretty graph.
10 You can do hypothesis testing. We may be interested in whether or not there is a correlation between two variables. Since samples are random, the sample correlation between two variables will show up as a little above or below zero by chance. How far from zero correlation does something have to be before it s significant?
11 This formula gives the t-score of correlation. The null hypothesis is: true correlation = zero. The alternative is: correlation not zero.
12 The t in this formula is the same t-score as in chapters 6 and 7. This t-score gets compared the critical values in the t-table at n-2 degrees of freedom.
13 The stronger the correlation, the farther r goes from zero. As r gets farther from zero, t-score gets bigger. So a stronger correlation gives you higher t-score. Stronger correlation better evidence of a correlation.
14 t-score also increases with sample size. As usual, it s under a square root. Having more data points makes it easier to detect correlations.
15 A larger t-score meant more evidence against the null, just like before. So a large t-score means more evidence of a correlation.
16 If there s a weak correlation and a small sample, we might not detect it. (Example: n=10, r=.25)
17 t* = 1.397, at 8 df, 0.20 significance. t* = 2.306, at 8 df, 0.05 significance. No significant evidence of a correlation. p > 0.20
18 What if we get a larger sample of this correlation? (n=46, r=0.25) We should get some evidence of a correlation, but not much.
19 t* = 1.684, at 44 df, 0.10 significance. t* = 2.021, at 44 df, 0.05 significance. Weak evidence of a correlation, 0.10 < p < 0.05.
20 What happens when you get a near perfect correlation? (Example: n=10, r=.99). Expectation: Very strong evidence of a correlation.
21 t* = 2.306, at 8 df, 0.05 significance. t* = 5.041, at 8 df, significance. Reality: Very strong evidence of a correlation.
22 The bottom gets very small, and dividing by a small number gives you something huge. The same thing happens with a near-perfect negative correlation, but the t-score is negative and huge.
23 For interest: You can always put a line exactly through two points. With only two points, we have no idea what the true correlation is. Points after the first two tell us about correlation. That s why correlation has n-2 degrees of freedom.
24 More math? More ugly sweaters! Show your pet some love by forcing it into a tea cosy.
25 First, we need to set down a convention. We re looking at two variables of the same object. We call these variables x and y. Example: If we were talking about dragons, X could be the length and Y could be the width. X is the independent/explanatory variable (the one we control or can measure more perfectly), Y is the dependent/response variable.
26 When x and y are correlated, we say that some of the variation in y is explained by x. Meaning: Across all the x, the range of y can be large.
27 But if we only consider a particular x (or a small x-interval), the range of y shrinks considerably. Y varies less for a particular X. Y has less variance when accounting for X.
28 r 2 is the proportion that the variance of y is reduced when accounting for x. r = 0.6 in this graph, so r 2 = = % of the variation in Y is explained by X.
29 The same proportion of variance is explained for a negative correlation of equal strength. A negative times itself is positive, so r 2 is always between 0 and 1.
30 In a perfect correlation, knowing x automatically gives you y as well. So there is no variation in y left to explain. r = 1 or -1, so r 2 = 1. All of the variation in y is explained by x. When two values are uncorrelated, using a linear function of x to guess at y is useless. r = 0, so r 2 = 0 None of the variation in y is explained by x.
31 The total squared difference from the mean of y is called the sum of squares total, or SST SST is the total square length of all the vertical red lines.
32 If we fit a line through the middle of the points in the scatter plot (called a regression line, the subject of chapter 11), the lines, on average, get shorter. The total squared length of these lines is the sum of squared error, or SSE.
33 The stronger the correlation, the shorter the vertical lines get. In other words, the smaller our errors get, and with them the Sum of Squared Error does too. Here, the correlation is very strong, and there are barely and errors at all.
34 r 2 can also be expressed in terms of SSE and SST. SST is the total amount of variation in Y SSE is the amount of variation in Y left unexplained by X. When r 2 is zero, SSE is same as SST When r 2 is one, SSE disappears completely.
35 An ugly sweater for every occasion! Even SPSS!
36 To find a correlation in SPSS, go to Analyze Correlate Bivariate (Means two-variable)
37 Pick the variables you want to correlate, drag them right. Pearson correlation coefficient MUST be selected. Spearman coefficient is optional.
38 There is a correlation of r =.940 between weight and height. It s a significant correlation, with a p-value of less than.001 (shows up as Sig. (2-tailed) =.000) Also, anything correlates with itself perfectly, so the correlation between length and length is r= 1
39 To build a scatterplot, go to graphs legacy dialogs Scatter/Dot
40 Choose Simple Scatter if it s not already picked, and click Define.
41 Move the independent variable into the x-axis, And the dependent variable into the y-axis,, then click OK (way at the bottom)
42 Our result: There is a definite upward trend, so the strong positive correlation of r = makes sense.
43 Next time: Residuals, Outliers and Influence, and the assumption of constant variance.
Slide 7.1. Theme 7. Correlation
Slide 7.1 Theme 7 Correlation Slide 7.2 Overview Researchers are often interested in exploring whether or not two variables are associated This lecture will consider Scatter plots Pearson correlation coefficient
More informationTHE PEARSON CORRELATION COEFFICIENT
CORRELATION Two variables are said to have a relation if knowing the value of one variable gives you information about the likely value of the second variable this is known as a bivariate relation There
More informationBusiness Statistics. Lecture 9: Simple Regression
Business Statistics Lecture 9: Simple Regression 1 On to Model Building! Up to now, class was about descriptive and inferential statistics Numerical and graphical summaries of data Confidence intervals
More informationy response variable x 1, x 2,, x k -- a set of explanatory variables
11. Multiple Regression and Correlation y response variable x 1, x 2,, x k -- a set of explanatory variables In this chapter, all variables are assumed to be quantitative. Chapters 12-14 show how to incorporate
More informationChapte The McGraw-Hill Companies, Inc. All rights reserved.
12er12 Chapte Bivariate i Regression (Part 1) Bivariate Regression Visual Displays Begin the analysis of bivariate data (i.e., two variables) with a scatter plot. A scatter plot - displays each observed
More informationOverview. Overview. Overview. Specific Examples. General Examples. Bivariate Regression & Correlation
Bivariate Regression & Correlation Overview The Scatter Diagram Two Examples: Education & Prestige Correlation Coefficient Bivariate Linear Regression Line SPSS Output Interpretation Covariance ou already
More informationLAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION
LAB 5 INSTRUCTIONS LINEAR REGRESSION AND CORRELATION In this lab you will learn how to use Excel to display the relationship between two quantitative variables, measure the strength and direction of the
More informationThe t-test: A z-score for a sample mean tells us where in the distribution the particular mean lies
The t-test: So Far: Sampling distribution benefit is that even if the original population is not normal, a sampling distribution based on this population will be normal (for sample size > 30). Benefit
More informationRegression Analysis. BUS 735: Business Decision Making and Research
Regression Analysis BUS 735: Business Decision Making and Research 1 Goals and Agenda Goals of this section Specific goals Learn how to detect relationships between ordinal and categorical variables. Learn
More informationOne sided tests. An example of a two sided alternative is what we ve been using for our two sample tests:
One sided tests So far all of our tests have been two sided. While this may be a bit easier to understand, this is often not the best way to do a hypothesis test. One simple thing that we can do to get
More informationBiostatistics: Correlations
Biostatistics: s One of the most common errors we find in the press is the confusion between correlation and causation in scientific and health-related studies. In theory, these are easy to distinguish
More informationChapter 19: Logistic regression
Chapter 19: Logistic regression Self-test answers SELF-TEST Rerun this analysis using a stepwise method (Forward: LR) entry method of analysis. The main analysis To open the main Logistic Regression dialog
More informationLecture (chapter 13): Association between variables measured at the interval-ratio level
Lecture (chapter 13): Association between variables measured at the interval-ratio level Ernesto F. L. Amaral April 9 11, 2018 Advanced Methods of Social Research (SOCI 420) Source: Healey, Joseph F. 2015.
More informationCan you tell the relationship between students SAT scores and their college grades?
Correlation One Challenge Can you tell the relationship between students SAT scores and their college grades? A: The higher SAT scores are, the better GPA may be. B: The higher SAT scores are, the lower
More informationChs. 16 & 17: Correlation & Regression
Chs. 16 & 17: Correlation & Regression With the shift to correlational analyses, we change the very nature of the question we are asking of our data. Heretofore, we were asking if a difference was likely
More informationOrdinary Least Squares Regression Explained: Vartanian
Ordinary Least Squares Regression Explained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent
More informationLAB 3 INSTRUCTIONS SIMPLE LINEAR REGRESSION
LAB 3 INSTRUCTIONS SIMPLE LINEAR REGRESSION In this lab you will first learn how to display the relationship between two quantitative variables with a scatterplot and also how to measure the strength of
More informationCorrelation. A statistics method to measure the relationship between two variables. Three characteristics
Correlation Correlation A statistics method to measure the relationship between two variables Three characteristics Direction of the relationship Form of the relationship Strength/Consistency Direction
More informationReview of Multiple Regression
Ronald H. Heck 1 Let s begin with a little review of multiple regression this week. Linear models [e.g., correlation, t-tests, analysis of variance (ANOVA), multiple regression, path analysis, multivariate
More informationUsing SPSS for One Way Analysis of Variance
Using SPSS for One Way Analysis of Variance This tutorial will show you how to use SPSS version 12 to perform a one-way, between- subjects analysis of variance and related post-hoc tests. This tutorial
More informationKeller: Stats for Mgmt & Econ, 7th Ed July 17, 2006
Chapter 17 Simple Linear Regression and Correlation 17.1 Regression Analysis Our problem objective is to analyze the relationship between interval variables; regression analysis is the first tool we will
More informationCorrelation and regression
NST 1B Experimental Psychology Statistics practical 1 Correlation and regression Rudolf Cardinal & Mike Aitken 11 / 12 November 2003 Department of Experimental Psychology University of Cambridge Handouts:
More informationBusiness Statistics. Lecture 10: Correlation and Linear Regression
Business Statistics Lecture 10: Correlation and Linear Regression Scatterplot A scatterplot shows the relationship between two quantitative variables measured on the same individuals. It displays the Form
More informationREVIEW 8/2/2017 陈芳华东师大英语系
REVIEW Hypothesis testing starts with a null hypothesis and a null distribution. We compare what we have to the null distribution, if the result is too extreme to belong to the null distribution (p
More informationWELCOME! Lecture 13 Thommy Perlinger
Quantitative Methods II WELCOME! Lecture 13 Thommy Perlinger Parametrical tests (tests for the mean) Nature and number of variables One-way vs. two-way ANOVA One-way ANOVA Y X 1 1 One dependent variable
More information9. Linear Regression and Correlation
9. Linear Regression and Correlation Data: y a quantitative response variable x a quantitative explanatory variable (Chap. 8: Recall that both variables were categorical) For example, y = annual income,
More informationRepeated-Measures ANOVA in SPSS Correct data formatting for a repeated-measures ANOVA in SPSS involves having a single line of data for each
Repeated-Measures ANOVA in SPSS Correct data formatting for a repeated-measures ANOVA in SPSS involves having a single line of data for each participant, with the repeated measures entered as separate
More informationOrdinary Least Squares Regression Explained: Vartanian
Ordinary Least Squares Regression Eplained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent
More informationMORE ON SIMPLE REGRESSION: OVERVIEW
FI=NOT0106 NOTICE. Unless otherwise indicated, all materials on this page and linked pages at the blue.temple.edu address and at the astro.temple.edu address are the sole property of Ralph B. Taylor and
More informationSIMPLE REGRESSION ANALYSIS. Business Statistics
SIMPLE REGRESSION ANALYSIS Business Statistics CONTENTS Ordinary least squares (recap for some) Statistical formulation of the regression model Assessing the regression model Testing the regression coefficients
More informationAMS 7 Correlation and Regression Lecture 8
AMS 7 Correlation and Regression Lecture 8 Department of Applied Mathematics and Statistics, University of California, Santa Cruz Suumer 2014 1 / 18 Correlation pairs of continuous observations. Correlation
More informationdetermine whether or not this relationship is.
Section 9-1 Correlation A correlation is a between two. The data can be represented by ordered pairs (x,y) where x is the (or ) variable and y is the (or ) variable. There are several types of correlations
More informationChapter 16. Simple Linear Regression and Correlation
Chapter 16 Simple Linear Regression and Correlation 16.1 Regression Analysis Our problem objective is to analyze the relationship between interval variables; regression analysis is the first tool we will
More informationChapter 8. Linear Regression. The Linear Model. Fat Versus Protein: An Example. The Linear Model (cont.) Residuals
Chapter 8 Linear Regression Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8-1 Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Fat Versus
More informationApplied Regression Analysis
Applied Regression Analysis Lecture 2 January 27, 2005 Lecture #2-1/27/2005 Slide 1 of 46 Today s Lecture Simple linear regression. Partitioning the sum of squares. Tests of significance.. Regression diagnostics
More informationStatistics Introductory Correlation
Statistics Introductory Correlation Session 10 oscardavid.barrerarodriguez@sciencespo.fr April 9, 2018 Outline 1 Statistics are not used only to describe central tendency and variability for a single variable.
More informationRegression Analysis: Basic Concepts
The simple linear model Regression Analysis: Basic Concepts Allin Cottrell Represents the dependent variable, y i, as a linear function of one independent variable, x i, subject to a random disturbance
More informationEstimating σ 2. We can do simple prediction of Y and estimation of the mean of Y at any value of X.
Estimating σ 2 We can do simple prediction of Y and estimation of the mean of Y at any value of X. To perform inferences about our regression line, we must estimate σ 2, the variance of the error term.
More informationModule 8: Linear Regression. The Applied Research Center
Module 8: Linear Regression The Applied Research Center Module 8 Overview } Purpose of Linear Regression } Scatter Diagrams } Regression Equation } Regression Results } Example Purpose } To predict scores
More informationCh. 1: Data and Distributions
Ch. 1: Data and Distributions Populations vs. Samples How to graphically display data Histograms, dot plots, stem plots, etc Helps to show how samples are distributed Distributions of both continuous and
More informationappstats27.notebook April 06, 2017
Chapter 27 Objective Students will conduct inference on regression and analyze data to write a conclusion. Inferences for Regression An Example: Body Fat and Waist Size pg 634 Our chapter example revolves
More informationr2, the coefficient of determination The bivariate normal assumption Diagnostic plots: Residuals and Cook's Distance R output (moved to week 3),
Today's Agenda r2, the coefficient of determination The bivariate normal assumption Diagnostic plots: Residuals and Cook's Distance R output (moved to week 3), Syllabus note: We are ahead of schedule in
More informationImportant note: Transcripts are not substitutes for textbook assignments. 1
In this lesson we will cover correlation and regression, two really common statistical analyses for quantitative (or continuous) data. Specially we will review how to organize the data, the importance
More informationIndependent Samples ANOVA
Independent Samples ANOVA In this example students were randomly assigned to one of three mnemonics (techniques for improving memory) rehearsal (the control group; simply repeat the words), visual imagery
More informationChapter Learning Objectives. Regression Analysis. Correlation. Simple Linear Regression. Chapter 12. Simple Linear Regression
Chapter 12 12-1 North Seattle Community College BUS21 Business Statistics Chapter 12 Learning Objectives In this chapter, you learn:! How to use regression analysis to predict the value of a dependent
More informationChapter 27 Summary Inferences for Regression
Chapter 7 Summary Inferences for Regression What have we learned? We have now applied inference to regression models. Like in all inference situations, there are conditions that we must check. We can test
More informationUpon completion of this chapter, you should be able to:
1 Chaptter 7:: CORRELATIION Upon completion of this chapter, you should be able to: Explain the concept of relationship between variables Discuss the use of the statistical tests to determine correlation
More informationCS 5014: Research Methods in Computer Science
Computer Science Clifford A. Shaffer Department of Computer Science Virginia Tech Blacksburg, Virginia Fall 2010 Copyright c 2010 by Clifford A. Shaffer Computer Science Fall 2010 1 / 207 Correlation and
More informationLECTURE 6. Introduction to Econometrics. Hypothesis testing & Goodness of fit
LECTURE 6 Introduction to Econometrics Hypothesis testing & Goodness of fit October 25, 2016 1 / 23 ON TODAY S LECTURE We will explain how multiple hypotheses are tested in a regression model We will define
More informationAP Statistics. Chapter 6 Scatterplots, Association, and Correlation
AP Statistics Chapter 6 Scatterplots, Association, and Correlation Objectives: Scatterplots Association Outliers Response Variable Explanatory Variable Correlation Correlation Coefficient Lurking Variables
More information14: Correlation. Introduction Scatter Plot The Correlational Coefficient Hypothesis Test Assumptions An Additional Example
14: Correlation Introduction Scatter Plot The Correlational Coefficient Hypothesis Test Assumptions An Additional Example Introduction Correlation quantifies the extent to which two quantitative variables,
More informationChapter 16. Simple Linear Regression and dcorrelation
Chapter 16 Simple Linear Regression and dcorrelation 16.1 Regression Analysis Our problem objective is to analyze the relationship between interval variables; regression analysis is the first tool we will
More informationChapter 8. Linear Regression. Copyright 2010 Pearson Education, Inc.
Chapter 8 Linear Regression Copyright 2010 Pearson Education, Inc. Fat Versus Protein: An Example The following is a scatterplot of total fat versus protein for 30 items on the Burger King menu: Copyright
More informationRegression used to predict or estimate the value of one variable corresponding to a given value of another variable.
CHAPTER 9 Simple Linear Regression and Correlation Regression used to predict or estimate the value of one variable corresponding to a given value of another variable. X = independent variable. Y = dependent
More informationUnivariate analysis. Simple and Multiple Regression. Univariate analysis. Simple Regression How best to summarise the data?
Univariate analysis Example - linear regression equation: y = ax + c Least squares criteria ( yobs ycalc ) = yobs ( ax + c) = minimum Simple and + = xa xc xy xa + nc = y Solve for a and c Univariate analysis
More informationInferences for Regression
Inferences for Regression An Example: Body Fat and Waist Size Looking at the relationship between % body fat and waist size (in inches). Here is a scatterplot of our data set: Remembering Regression In
More informationMA 1125 Lecture 15 - The Standard Normal Distribution. Friday, October 6, Objectives: Introduce the standard normal distribution and table.
MA 1125 Lecture 15 - The Standard Normal Distribution Friday, October 6, 2017. Objectives: Introduce the standard normal distribution and table. 1. The Standard Normal Distribution We ve been looking at
More informationdf=degrees of freedom = n - 1
One sample t-test test of the mean Assumptions: Independent, random samples Approximately normal distribution (from intro class: σ is unknown, need to calculate and use s (sample standard deviation)) Hypotheses:
More informationRegression Analysis. Regression: Methodology for studying the relationship among two or more variables
Regression Analysis Regression: Methodology for studying the relationship among two or more variables Two major aims: Determine an appropriate model for the relationship between the variables Predict the
More informationLecture 16 - Correlation and Regression
Lecture 16 - Correlation and Regression Statistics 102 Colin Rundel April 1, 2013 Modeling numerical variables Modeling numerical variables So far we have worked with single numerical and categorical variables,
More informationFinding Relationships Among Variables
Finding Relationships Among Variables BUS 230: Business and Economic Research and Communication 1 Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions, hypothesis
More information1 A Review of Correlation and Regression
1 A Review of Correlation and Regression SW, Chapter 12 Suppose we select n = 10 persons from the population of college seniors who plan to take the MCAT exam. Each takes the test, is coached, and then
More informationSingle and multiple linear regression analysis
Single and multiple linear regression analysis Marike Cockeran 2017 Introduction Outline of the session Simple linear regression analysis SPSS example of simple linear regression analysis Additional topics
More informationResiduals, Coefficient of Determination Worksheet Solutions
Math 121 Ravenwood Residuals, Coefficient of Determination Worksheet Solutions Atmospheric Temperature as a Function of Altitude (not real data) Which means the linear regression equation is 6.488 14.977,
More informationCS 147: Computer Systems Performance Analysis
CS 147: Computer Systems Performance Analysis Advanced Regression Techniques CS 147: Computer Systems Performance Analysis Advanced Regression Techniques 1 / 31 Overview Overview Overview Common Transformations
More informationRegression, part II. I. What does it all mean? A) Notice that so far all we ve done is math.
Regression, part II I. What does it all mean? A) Notice that so far all we ve done is math. 1) One can calculate the Least Squares Regression Line for anything, regardless of any assumptions. 2) But, if
More informationExploratory Factor Analysis and Principal Component Analysis
Exploratory Factor Analysis and Principal Component Analysis Today s Topics: What are EFA and PCA for? Planning a factor analytic study Analysis steps: Extraction methods How many factors Rotation and
More information7.2 One-Sample Correlation ( = a) Introduction. Correlation analysis measures the strength and direction of association between
7.2 One-Sample Correlation ( = a) Introduction Correlation analysis measures the strength and direction of association between variables. In this chapter we will test whether the population correlation
More informationReview of Statistics 101
Review of Statistics 101 We review some important themes from the course 1. Introduction Statistics- Set of methods for collecting/analyzing data (the art and science of learning from data). Provides methods
More informationDraft Proof - Do not copy, post, or distribute. Chapter Learning Objectives REGRESSION AND CORRELATION THE SCATTER DIAGRAM
1 REGRESSION AND CORRELATION As we learned in Chapter 9 ( Bivariate Tables ), the differential access to the Internet is real and persistent. Celeste Campos-Castillo s (015) research confirmed the impact
More informationt-test for b Copyright 2000 Tom Malloy. All rights reserved. Regression
t-test for b Copyright 2000 Tom Malloy. All rights reserved. Regression Recall, back some time ago, we used a descriptive statistic which allowed us to draw the best fit line through a scatter plot. We
More informationBivariate Relationships Between Variables
Bivariate Relationships Between Variables BUS 735: Business Decision Making and Research 1 Goals Specific goals: Detect relationships between variables. Be able to prescribe appropriate statistical methods
More informationBusiness Statistics. Lecture 10: Course Review
Business Statistics Lecture 10: Course Review 1 Descriptive Statistics for Continuous Data Numerical Summaries Location: mean, median Spread or variability: variance, standard deviation, range, percentiles,
More informationDescribing the Relationship between Two Variables
1 Describing the Relationship between Two Variables Key Definitions Scatter : A graph made to show the relationship between two different variables (each pair of x s and y s) measured from the same equation.
More informationChs. 15 & 16: Correlation & Regression
Chs. 15 & 16: Correlation & Regression With the shift to correlational analyses, we change the very nature of the question we are asking of our data. Heretofore, we were asking if a difference was likely
More informationMultiple Regression Analysis
Multiple Regression Analysis y = β 0 + β 1 x 1 + β 2 x 2 +... β k x k + u 2. Inference 0 Assumptions of the Classical Linear Model (CLM)! So far, we know: 1. The mean and variance of the OLS estimators
More informationSimple Linear Regression
Simple Linear Regression 1 Correlation indicates the magnitude and direction of the linear relationship between two variables. Linear Regression: variable Y (criterion) is predicted by variable X (predictor)
More informationThe simple linear regression model discussed in Chapter 13 was written as
1519T_c14 03/27/2006 07:28 AM Page 614 Chapter Jose Luis Pelaez Inc/Blend Images/Getty Images, Inc./Getty Images, Inc. 14 Multiple Regression 14.1 Multiple Regression Analysis 14.2 Assumptions of the Multiple
More information1 Correlation and Inference from Regression
1 Correlation and Inference from Regression Reading: Kennedy (1998) A Guide to Econometrics, Chapters 4 and 6 Maddala, G.S. (1992) Introduction to Econometrics p. 170-177 Moore and McCabe, chapter 12 is
More informationStatistics and Quantitative Analysis U4320. Lecture 13: Explaining Variation Prof. Sharyn O Halloran
Statistics and Quantitative Analysis U4320 Lecture 13: Eplaining Variation Prof. Sharyn O Halloran I. Eplaining Variation: R 2 A. Breaking Down the Distances Let's go back to the basics of regression analysis.
More informationCorrelation. January 11, 2018
Correlation January 11, 2018 Contents Correlations The Scattterplot The Pearson correlation The computational raw-score formula Survey data Fun facts about r Sensitivity to outliers Spearman rank-order
More informationStatistics and Quantitative Analysis U4320
Statistics and Quantitative Analysis U3 Lecture 13: Explaining Variation Prof. Sharyn O Halloran Explaining Variation: Adjusted R (cont) Definition of Adjusted R So we'd like a measure like R, but one
More informationRegression Analysis II
Regression Analysis II Measures of Goodness of fit Two measures of Goodness of fit Measure of the absolute fit of the sample points to the sample regression line Standard error of the estimate An index
More informationQuantitative Understanding in Biology Module II: Model Parameter Estimation Lecture I: Linear Correlation and Regression
Quantitative Understanding in Biology Module II: Model Parameter Estimation Lecture I: Linear Correlation and Regression Correlation Linear correlation and linear regression are often confused, mostly
More informationKeppel, G. & Wickens, T. D. Design and Analysis Chapter 4: Analytical Comparisons Among Treatment Means
Keppel, G. & Wickens, T. D. Design and Analysis Chapter 4: Analytical Comparisons Among Treatment Means 4.1 The Need for Analytical Comparisons...the between-groups sum of squares averages the differences
More informationWISE Regression/Correlation Interactive Lab. Introduction to the WISE Correlation/Regression Applet
WISE Regression/Correlation Interactive Lab Introduction to the WISE Correlation/Regression Applet This tutorial focuses on the logic of regression analysis with special attention given to variance components.
More information11 Correlation and Regression
Chapter 11 Correlation and Regression August 21, 2017 1 11 Correlation and Regression When comparing two variables, sometimes one variable (the explanatory variable) can be used to help predict the value
More informationSimple Linear Regression: One Quantitative IV
Simple Linear Regression: One Quantitative IV Linear regression is frequently used to explain variation observed in a dependent variable (DV) with theoretically linked independent variables (IV). For example,
More informationCorrelation. We don't consider one variable independent and the other dependent. Does x go up as y goes up? Does x go down as y goes up?
Comment: notes are adapted from BIOL 214/312. I. Correlation. Correlation A) Correlation is used when we want to examine the relationship of two continuous variables. We are not interested in prediction.
More informationCh. 16: Correlation and Regression
Ch. 1: Correlation and Regression With the shift to correlational analyses, we change the very nature of the question we are asking of our data. Heretofore, we were asking if a difference was likely to
More informationRelationships between variables. Association Examples: Smoking is associated with heart disease. Weight is associated with height.
Relationships between variables. Association Examples: Smoking is associated with heart disease. Weight is associated with height. Income is associated with education. Functional relationships between
More informationLectures on Simple Linear Regression Stat 431, Summer 2012
Lectures on Simple Linear Regression Stat 43, Summer 0 Hyunseung Kang July 6-8, 0 Last Updated: July 8, 0 :59PM Introduction Previously, we have been investigating various properties of the population
More informationappstats8.notebook October 11, 2016
Chapter 8 Linear Regression Objective: Students will construct and analyze a linear model for a given set of data. Fat Versus Protein: An Example pg 168 The following is a scatterplot of total fat versus
More informationPsychology 282 Lecture #4 Outline Inferences in SLR
Psychology 282 Lecture #4 Outline Inferences in SLR Assumptions To this point we have not had to make any distributional assumptions. Principle of least squares requires no assumptions. Can use correlations
More informationEM375 STATISTICS AND MEASUREMENT UNCERTAINTY CORRELATION OF EXPERIMENTAL DATA
EM375 STATISTICS AND MEASUREMENT UNCERTAINTY CORRELATION OF EXPERIMENTAL DATA In this unit of the course we use statistical methods to look for trends in data. Often experiments are conducted by having
More informationNote that we are looking at the true mean, μ, not y. The problem for us is that we need to find the endpoints of our interval (a, b).
Confidence Intervals 1) What are confidence intervals? Simply, an interval for which we have a certain confidence. For example, we are 90% certain that an interval contains the true value of something
More informationHUDM4122 Probability and Statistical Inference. February 2, 2015
HUDM4122 Probability and Statistical Inference February 2, 2015 Special Session on SPSS Thursday, April 23 4pm-6pm As of when I closed the poll, every student except one could make it to this I am happy
More informationLecture 3. The Population Variance. The population variance, denoted σ 2, is the sum. of the squared deviations about the population
Lecture 5 1 Lecture 3 The Population Variance The population variance, denoted σ 2, is the sum of the squared deviations about the population mean divided by the number of observations in the population,
More informationAnalysis of Variance (ANOVA)
Analysis of Variance (ANOVA) Two types of ANOVA tests: Independent measures and Repeated measures Comparing 2 means: X 1 = 20 t - test X 2 = 30 How can we Compare 3 means?: X 1 = 20 X 2 = 30 X 3 = 35 ANOVA
More informationWhat is a Hypothesis?
What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population mean Example: The mean monthly cell phone bill in this city is μ = $42 population proportion Example:
More information