# TB6/7 RM Topic Overview

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• Created by: mint75
• Created on: 17-11-15 15:42
• RM TB6/7 Overview
• Linear Regression
• A way of predicting outcomes you have not measured
• Creates a linear model of the relationship between two variables
• What to look for
• R(squared)= The % of variance accounted for by the model
• SSM (SST/SSR)= The amount of improvement by using the 'best' model over the 'dumb' model
• The F Ratio = The ratio of the MSM (regression) error to the mean square residual error. A larger F = smaller p value
• y = b1x + b0
• Correlation
• A way of measuring the extent to which two variables are related
• DOES NOT IMPLY CAUSATION
• What to look for
• Correlation Coefficient (r) = Divide the covariance by the product of the individual STDDES
• Should always be between -1 and +1, 0 = no relationship.
• A standardised measure of the size AND direction of the relationship
• Covariance = Sum of the cross-product deviations, divided by n -  1
• Tells you the DIRECTION but not size of the relationship
• Non-parametric alternatives
• Spearmans Rho (assumptions violated)
• Kendalls Tau (small data set with tied ranks)
• Partial correlations
• Used to control for other potential mediating variables, the EXCLUSIVE relationship of x to y
• Multiple Regression
• The multiple regression equation
• y = b0 + b1x1 + b2x2 +...bnxn + residuals (eta)
• Different methods of regression
• Managing the order of variables you're fitting
• Forced Entry
• Hierarchical
• Stepwise
• Interpreting multiple regression
• R2 - The proportion of variance accounted for by the model
• Adjusted R2 = An estimate of R2 in the population (shrinkage)
• You want these to be similar, meaning the model could generalise to the population
• ANOVA F Statistic; Tells us whether the regression model is a better predictor than the mean (dumb) model
• Beta Values
• The change in the outcome associted with a unit change in the predictor
• Standardised beta values = the same but as STDDEV
• The change in the outcome associted with a unit change in the predictor
• Predicts the values of an outcome variable from several predictors
• How well does the model fit the data?
• Residual statistics (Standardised residuals)
• Confidence intervals, 1.96+-
• Influential cases (Cooks distance)
• Measures the influence of a single case on the whole model, values > 1 = bad
• Standardised Beta Values
• A beta value tells us the CHANGE in the outcome variable associated with unit change in predictor
• The standardised betas tell us the same but expressed as a STDDEV
• e.g B1 = 0.523, as adverts increased by 1 STDDEV, sales increased by 0.523 of a STDDEV
• These allow us to directly compare the effects of variables
• e.g b1 = 0.087, as adverts incresed by £100 sales increased by 0.087 units
• Factor Analysis
• Tests for 'clusters' of variables. Which measures are ASPECTS of a common dimension? How many are there?
• Use correlation (R) matrix
• Aiming to reduce the R-matrix into SMALL sets of UN-CORRELATED dimensions
• How much does each question contribute to each factor?
• Principal Component Analysis (PCA) = finds the principal axis of a cloud of data points, allowing you to find factors (FA)
• Use Eigenvectors, reduce multidimensional data sets into a set of components
• Eigenvalues tell you how important each eigenvector is
• Scree Plots
• Look for the point of inflexion, as opposed to Kaiser extraction where you only use eigenvalues > 1
• Rotation
• Maximises the loading of a variable on one factor whilst minimising load on all other factors
• Orthoganol (VARIMAX) both axes are rotated to go through the center of the clouds, factors are UNCORRELATED
• Reliability
• Test-retest method and Split half method
• Cronbachs alpha, data is reliable if a > 0.7
• Although affected by number of items
• Reverse score reverse phrased items!
• Also note assumptions of each test