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Guide to Multiple Regression Analysis Study Guide

This guide provides a comprehensive overview of multiple regression, a statistical technique used to model the relationship between a dependent variable and two or more independent variables. It details key metrics such as R-squared and standardized coefficients, explores various regression methods including hierarchical and stepwise approaches, and discusses essential assumptions and diagnostic tools like multicollinearity and VIF. The guide also covers techniques for estimating and validating

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Statistical Methods in Kinesiology Regression and Correlation

Multiple Regression in Kinesiology

Multiple regression involves calculating, interpreting, and presenting findings from models with a single dependent variable and multiple independent variables.

  • Multiple regression
  • Forced regression
  • Hierarchical regression
  • Stepwise regression
  • Partial correlations
  • Standard error of the estimate
  • Predicted value
  • Confidence interval
  • Cross validation
  • Multiple correlation coefficient squared
  • Beta weights
  • Normality of residuals
  • Homoscedasticity of residuals
  • Multicollinearity
  • Singularity
  • Zero-order correlation
  • Semi-partial correlation

Statistical Methods in Multiple Regression

This content covers types of multiple regression, including hierarchical, stepwise, and standard methods, alongside concepts like multicollinearity and standardized coefficients.

  • Standard multiple regression
  • Hierarchical multiple regression
  • Forward multiple regression
  • Backward multiple regression
  • Stepwise multiple regression
  • Correlation Matrix
  • Multicollinearity
  • VIF
  • Standardized Coefficients
  • Partial correlations
  • Dummy code
  • Isokinetic torque

Multiple Regression Estimation and Validation

Using regression equations for predicting unknown values through estimation, calculating the standard error of the estimate, and performing cross validation.

  • Estimation
  • Regression equation
  • Standard deviation of residuals
  • Standard Error of the Estimate (SEE)
  • Confidence Interval
  • Cross Validation
  • Constant Error
  • Total Error

Statistical Methods in Kinesiology Correlation

This material covers the characteristics, interpretation, and assumptions of product moment correlation coefficient and scatterplots.

  • Product moment correlation coefficient
  • Correlation coefficient r
  • Coefficient of determination r2
  • Scatterplots
  • Strength and direction of linear relationships
  • Positive and negative correlation
  • Assumptions of correlation
  • Interval and ratio data
  • Normal distribution
  • Homoscedasticity and heteroscedasticity
  • Linear and curvilinear relationships
  • Z scores
  • Line of best fit

Calculating and Interpreting Correlation Coefficients

Statistical methods in kinesiology for calculating the product moment correlation coefficient, determining statistical significance, and evaluating the coefficient of determination.

  • Product moment
  • Correlation coefficient
  • Statistical significance
  • p value
  • Null hypothesis
  • Coefficient of determination
  • Common variance
  • Qualitative evaluation
  • Quantitative evaluation
  • Linear relationship
  • Curvilinear relationship
  • Range restriction
  • Cause and effect

Comparing Means Using T Tests

Calculate and interpret three types of t tests to assess differences between two sets of values and determine if differences are real or due to chance.

  • Independent Samples T Test
  • Dependent/Paired/Related Samples T Test
  • One Sample T Test
  • Null Hypothesis
  • Research Hypothesis
  • Effect Size
  • Cohen’s d
  • Type I Error
  • Type II Error
  • Power
  • Alpha level
  • Homogeneity of variance
  • Parametric data
  • Standard error of the difference
  • Degrees of freedom
  • One-Tailed vs. Two-Tailed tests

Bivariate Regression Statistical Methods

Bivariate regression is the statistical development of a regression equation to predict the variance in Y from the variance in X.

  • Bivariate regression
  • Simple linear regression
  • Predictor variable
  • Dependent variable
  • Independent variable
  • Scatterplot
  • Regression equation
  • Slope
  • Y-intercept
  • Line of best fit
  • Residuals
  • Correlation coefficient
  • Coefficient of determination
  • Standard error of the estimate
  • Homoscedasticity
  • Heteroscedasticity
  • Normality of residuals
  • F-test
  • t statistic

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