PDF-Linear Regression and Correlation NotesSuppose there is a data set of

2Note that1r1otal Sum of Squares TSS of the data set asTSSni1Syiy2note thatTSSSyygression SSR asRSSni1Syiy2and note that sinceyiwill not be exactly on the regression lineTSSx0000RSSunless the poi. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. Bivariate. Data . With Fathom. *. CFU 3102.5.10 Using technology with a set of contextual linear data to examine the line of best fit;. determine and interpret the correlation coefficient.. Andy Wilson – APSU – . What is an association between variables?. Explanatory and response variables. Key characteristics of a data set. 1. Association between a pair of variables. Association:. Some values of one variable tend to occur more often with certain values of the other variable. An Application. Dr. Jerrell T. Stracener, . SAE Fellow. Leadership in Engineering. EMIS 7370/5370 STAT 5340 :. . . PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS. Systems Engineering Program. Andrea . Banino. & Punit . Shah . Samples . vs. Populations . Descriptive . vs. Inferential. William Sealy . Gosset. (‘Student’). Distributions, probabilities and P-values. Assumptions of t-tests. How to predict and how it can be used in the social and behavioral sciences. How to judge the accuracy of predictions. INTERCEPT and SLOPE functions. Multiple regression. This week. 2. Based on the correlation, you can predict the value of one variable from the value of another.. What is Correlation Analysis?. Testing the Significance of the Correlation Coefficient . Regression Analysis. The Standard Error of Estimate . Assumptions Underlying Linear Regression. Confidence and Prediction Intervals. Correlation and regression are powerful tools, but have limitations.. Correlation and regression describe only linear relationship.. Correlation r and the least-squares regression are not resistant. . Model . the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed . data.. Formally, the model for multiple linear regression, given . 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) . using a linear equation.. Linear Regression Formula: . Used for prediction purposes for values beyond the region of the given data.. Equation: . and . are the means of x and y. is the standard deviation of x. is the covariance. Instructor: Prof. Wei Zhu. 11/21/2013. AMS 572 Group Project. Motivation & Introduction – Lizhou Nie. A Probabilistic Model for Simple Linear Regression – Long Wang. Fitting the Simple Linear Regression Model – . Nisheeth. Linear regression is like fitting a line or (hyper)plane to a set of points. The line/plane must also predict outputs the unseen (test) inputs well. . Linear Regression: Pictorially. 2. (Feature 1). Regression Trees. Characteristics of classification models. model. linear. parametric. global. stable. decision tree. no. no. no. no. logistic regression. yes. yes. yes. yes. discriminant. analysis.