Introduction to Linear Regression and Correlation Analysis

Introduction to Linear Regression and Correlation Analysis Goals After this, you should be able to: †¢ †¢ †¢ †¢ †¢ Calculate and interpret the simple correlation between two variables Determine whether the correlation is significant Calculate and interpret the simple linear regression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant Goals (continued) After this, you should be able to: †¢ Calculate and interpret confidence intervals for the regression coefficients †¢ Recognize regression analysis applications for purposes of prediction and description †¢ Recognize some potential problems if regression analysis is used incorrectly †¢ Recognize†¦show more content†¦sed to: – Predict the value of a dependent variable based on the value of at least one independent variable – Explain the impact of changes in an independent variable on the dependent variable Dependent variable: the variable we wish to explain Independent variable: the variable used Simple Linear Regression Model †¢ Only one independent variable, x †¢ Relationship between x and y is described by a linear function †¢ Changes in y are assumed to be caused by changes in x Types of Regression Models Positive Linear Relationship Relationship NOT Linear Negative Linear Relationship No Relationship Population Linear Regression The population regression model: Population y intercept Dependent Variable Population Slope Coefficient Independent Variable y ï€ ½ ÃŽ ²0 ï€ « ÃŽ ²1x ï€ « ÃŽ µ Linear component Random Error term, or residual Random Error component Linear Regression Assumptions †¢ Error values (ÃŽ µ) are statistically independent †¢ Error values are normally distributed for any given value of x †¢ The probability distribution of the errors is normal †¢ The probability distribution of the errors has constant variance †¢ The underlying relationship between the x Population Linear Regression y Observed Value of y for xi y ï€ ½ ÃŽ ²0 ï€ « ÃŽ ²1x ï€ « ÃŽ µ ÃŽ µi (continued) Slope = ÃŽ ²1 Random Error for this x value Predicted Value of y for xi Intercept = ÃŽ ²0 xi x Estimated Regression Model The sample regression line provides an estimate of theShow MoreRelatedIterative Multivariate Regression For Correlated Responses1246 Words   |  5 PagesIterative Multivariate Regression for Correlated Responses Multivariate regression is a standard statistical tool that regresses independent variables (predictors) against a single dependent variable (response variable).The objective is to find a linear model that best predicts the dependent variable from the independent variables. 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