PPT-Simple Linear Regression & Correlation

Instructor Prof Wei Zhu 11212013 AMS 572 Group Project Motivation amp Introduction Lizhou Nie A Probabilistic Model for Simple Linear Regression Long Wang Fitting the Simple Linear Regression Model . Jennifer Kensler. Laboratory for Interdisciplinary Statistical Analysis. Collaboration. . From our website request a meeting for personalized statistical advice. Great advice right now:. Meet with LISA . ... beware. Definition. Var. (X+Y) = . Var. (X) + . Var. (Y) + 2·Cov(X,Y). The . correlation. between two random variables is a dimensionless number between 1 and -1.. Interpretation. Correlation measures the . Linear Function. Y = a + bX. Fixed and Random Variables. A FIXED variable is one for which you have every possible value of interest in your sample.. Example: Subject sex, female or male.. A RANDOM variable is one where the sample values are randomly obtained from the population of values.. NBA 2013/14 Player Heights and Weights. Data Description / Model. Heights (X) and Weights (Y) for 505 NBA Players in 2013/14 Season. . Other Variables included in the Dataset: Age, Position. Simple Linear Regression Model: Y = . Var. (X Y) = . Var. (X) . Var. (Y) 2·Cov(X,Y). The . correlation. between two random variables is a dimensionless number between 1 and -1.. Interpretation. Correlation measures the . strength. of the . Prepared by T.O. . Antwi. -Asare . 2/2/2017. 1. Correlation and Regression . Correlation. Scatter Diagram,. Karl Pearson Coefficient of Correlation. Rank Correlation. Limits for Correlation Coefficient. 9-. 1. 2. Objectives. Understand the basic types of data. Conduct basic statistical analyses in Excel. Generate descriptive statistics and other analyses using the Analysis . ToolPak. Use regression analysis to predict future values. 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.. What. is . what. ? . Regression: One variable is considered dependent on the other(s). Correlation: No variables are considered dependent on the other(s). Multiple regression: More than one independent variable. 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. -2-Note that-1r1otal Sum of Squares TSS of the data set asTSSni1Syi-y2note thatTSSSyygression SSR asRSSni1Syi-y2and note that sinceyiwill not be exactly on the regression lineTSSx0000RSSunless the poi Simple Linear Regression. April 17, 2018. Correlation . analysis* . M. easuring the degree . of association between two . continuous variables. , x and . y. We . have a . linear relationship. between x and y . 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.